The Guardian also covered the claims on 23 Sep 2014; they were apparently 3 or 4 different claims, although some were about the same locations. In summary, some of the claims were individually debunked by the "Yes" campaign, and more generally even the SNP leadership (which had supported the "Yes") disavowed the idea that vote counting was flawed or rigged:
On Twitter and YouTube, in blog posts and Facebook groups, sceptics have been amassing what they believe is evidence that the referendum was rigged, and its result, therefore, illegitimate.
Many refer to a snippet of video in which a counting officer at the Dundee polling station appears to lift votes from a yes pile and place them under no.
Another widely circulated photograph from the Dundee count appears to show a yes vote, bundled with others, sitting in the no pile. [...]
Others refer to footage that they claim shows a counting officer in Edinburgh writing on a ballot paper.
For many, the fire alarms that caused the brief evacuation of the Dundee count, and the fact that a Russian observer from a pro-Kremlin monitoring agency had claimed the ballot was fixed to avoid parallels to the situation in Crimea, were taken as further causes for suspicion.
All of the apparently suspicious evidence could be easily explained, said a spokeswoman, pointing out that the yes campaign itself had intervened on Twitter on Thursday night to reassure voters that there was nothing awry with the Dundee footage.
At times, uncounted ballots would be placed on tables that had yes or no signs attached before being sorted, she said. And piles that didn’t reach round numbers of 50 or 100 would be wrapped in a piece of paper on which the total number of votes would be written, explaining the Edinburgh footage.
In a statement, the chief counting officer, Mary Pitcaithly, said she was “satisfied that all counts throughout Scotland were properly conducted and scrutinised by thousands of people representing both the Yes Scotland and the Better Together campaigns, as well as international election observers, media and police. None of these people raised any concerns during the verification, counting and adjudication stages.”
Salmond may have claimed over the weekend that no voters were “gulled” and “tricked” into rejecting independence, but a spokesman said that neither he nor the SNP believed there was anything untoward about the count itself.
No mainstream news articles have covered the specific claims made in relation to those videos after that Guardian article, it seems.
Despite this, there was fairly widespread popular belief that some fraud took place, as evidenced in some Dec 2014 polls. (12% thought "a lot" fraud took place, and 22 thought "a little" fraud happened.) The plurality of those who answered this question positively (36% of them) attributed their belief to stories they had read in the media. There was also an 100,000 strong on-line petition calling for a recount. As far as I know this call for a recount was not endorsed by a major party and was not given course. (Also, 19% of the people polled before the referendum believed it was going to be rigged.)
There was another video claim posted in October when a man said he found "Yes" votes in a trash bin in Glasgow. I haven't found any follow-up in the mass media on that particular case, even though the police had launched an investigation, but the SNP reacted to it (in the initial story) by reiterating that
they accept the result of the referendum and that the electoral commission’s measures were “fair and robust”. They refused to comment on any specific allegations made by voters about the electoral process.
Finally, the law enabling the referendum provided explicitly only for local recounts. None such recounts were requested however. From the official final report on referendum (published in December):
No recounts were requested locally and given the work undertaken by COs and their staff and observations undertaken in count centres by Commission representatives it is clear that all local totals were accepted by those agents present locally. Once the local results were accepted then it followed that acceptance of each of the 32 local counting area results, once totalled, led to a translation of local confidence in the local total into confidence in the national result.
Also this setup of the recount system was not novel, it was previously used in other referendums in the UK:
Many were unaware and surprised to learn that, although the SIRA [Scottish Independence Referendum Act]
authorised COs to recount votes in their local counting area and also allowed
the CCO to require them to recount, there was no explicit provision in the
legislation for a national recount. No provision existed for the CCO to require
any CO to recount the votes if the totals for the counting area had already
been certified and declared. These provisions largely mirrored those in the
PVSC Act 2011 and the provisions in the National Assembly for Wales
Referendum (Assembly Act Provisions) (Referendum Question, Date of
Referendum etc.) Order 2010 which set the rules for the referendum held in
Wales in 2011.
Although the OP didn't asking about this, for completeness, I'll mention that later on, in 2015 a pro-independence article in the Scottish Standard website claimed that there had been fraud using postal ballots, using the statistics from the Argyll & Bute area for their argument. The Conservative-leaning Telegraph wrote of these claims dismissively a bit later
In the front window of Dunoon’s Scottish National Party campaign base, alongside posters and canvassing information for the local SNP candidate, Brendan O’Hara, they’re displaying for sale a new pamphlet which describes in detail how MI5 and John McTernan, chief of staff to Jim Murphy, the Scottish Labour leader, “rigged” last year’s independence referendum by creating thousands of fake No ballot papers.
The authors, nationalist activists from Argyll, first suspected the existence of the “McTernan Plan”, as they call it, on the night of the count. Their “extensive canvass returns” had left them “confident of success” in the area, but when the postal vote came in they were “astounded” to discover it was 70-30 against independence. What’s more, the postal voter turnout in Argyll was 96.4 per cent. “We had never before heard of such a high return in any democratic election,” they said.
The activists’ suspicions hardened when they learned that Mr McTernan, then a Labour commentator, had appeared on TV four days before the referendum saying that “postal votes are running very strongly towards No.”
“I couldn’t work out how it was possible to interfere on any scale with the postal ballot,” Andy Anderson, one of the authors, told the Telegraph. “You need the ballot paper number, the signature and date of birth of the voter. Then it occurred to me. All that information went into a computer – and who’s at the other end of the computer in London? MI5.” [...]
Rather more likely, of course, is that the Yes campaign’s canvas returns were wrong. The overall No vote in Argyll and Bute was a convincing 58.5 per cent, on an 88.2 per cent turnout, with the vast majority of votes cast in person. Postal voters are often more conservative than in-person voters, since they are older and more rural. And postal vote turnouts are always higher than overall turnouts; those motivated enough to apply for a postal vote are also more motivated to use it.
Mr McTernan’s foreknowledge is easily explained, too: though the postal votes were not actually counted until referendum night, they were opened beforehand, with campaign representatives present and able to peek at where people put their crosses. The No margin of victory was almost 400,000 votes, so MI5 would have had to visit an awful lot of postboxes.
No other widely-circulated newspapers seem to have covered this postal claim.
The UK allowed Russian observers from the Russian Public Institute of Electoral Law (ROIIP) to monitor the Scottish referendum. These have criticized various aspects of it, and their criticism was reproduced by Western mass media, however an article in OCCRP... criticized these ROIIP observers as obviously lacking impartiality based on their pre-election comments, as well as based on their long-term track record. Furthermore the ROIIP reports are contradicted by those of other observers, present at the same events.
The day before the vote, delegation member Alexey Martynov, who heads a Moscow body called The International Institute of Newly Established States, was casting a critical eye on proceedings.
He mused on Facebook: “Interesting that almost 750,000 people registered to vote in advance by postal vote. That is nearly 17 percent. Who was it who was screaming about too big an advance vote at last Sunday’s elections in Russia?”
The Electoral Commission’s code of conduct requires observers to maintain “strict political impartiality at all times.” In another comment on Facebook, also posted before the counting was finished, Martynov declared: “It’s clear they will cheat.”
Vitaliy Kovin of Golos, an independent Russian electoral rights group that also attended the vote as observers, said the ROIIP delegation behaved strangely during the vote count.
Kovin said he did not see the ROIIP team at the Electoral Commission’s guidance event for electoral observers, but did spot them talking in the hangar where the Edinburgh count took place.
He told OCCRP that, since the count was organized very differently from proceedings in Russia, it was natural that international observers should ask for some things to be explained.
“But,” Kovin added, “[the ROIIP delegation’s] conversations were very skeptical and critical. ‘What is this mess, this chaos? These people are running about, some people are bringing something. Other people are sitting behind tables – who are they?’”
It was a moment in which the people of Scotland were vulnerable, says independence campaigner Douglas Daniel, who was present at the vote count and wrote about it for the political website Wings Over Scotland.
At the time, he says, he knew nothing about the ROIIP team.
“It wasn't until the articles speaking about ‘Russia’ and saying the process was flawed [appeared] that I became aware of their existence,” says Daniel.
Sure enough, by the end of the day after the vote, the ROIIP delegation’s damning verdict was all over the British and Russian press.
The vote in Scotland “[did] not conform to generally accepted international principles of referendums,” said Borisov, the delegation’s head.
He claimed it was “impossible to see what is going on at [polling tables]”. Worse, ballot boxes were “lying around… without any protection.” [...]
Borisov’s comments were the first post made on the Facebook page of the group “Rally for a Revote,” which was linked to a petition that collected more than 100,000 signatures.
But the Russian delegation’s view was at odds with those of other observers.
Adrian Browarczyk, who led a monitoring team from the European Students Forum, told OCCRP, “We assessed this referendum as fair and free of fraud… No one from my team reported anything that would be in line with Borisov’s accusations.”
Browarczyk, who also observed elections in 2014 in Ukraine and Moldova, said the Russian claims did not surprise him.
“I believe Borisov intentionally criticized the proceedings from the counting [station],” he said, adding: “It is an obvious way Kremlin-backed bodies behave in order to undermine the values that Europe cherishes.”
The OCCRP article goes on to detail how Borisov basically backed the Kremlin's position in quite a few contested election in Russia and neighboring countries. It's a little too long (and perhaps rather off-topic) to reproduce all that here.
A 2017 article in Medium compared the numbered of signatures the petitions related to the Scottish referndum received:
The petitions received very different levels of support. The declaration of independence gathered 3,888 signatures. The call for a [judicial] review gathered 25,905. The Yes2014 version had 18,821 signatures by September 21. The petition to the UK Parliament had 23,697 signatures by March 2015.
Far more than any of these, however, the “Rally for a Revote” petition gathered 100,261 signatures by the time it closed.
This is a remarkably high figure, given that total turnout in the referendum was 3.6 million, and given that the formal petition to the UK Parliament achieved less than a quarter of the impact. It raises the question of whether an attempt was made to artificially amplify the signatures. [...]
Change.org only requires an email address and name to sign petitions. @DFRLab asked Change.org twice how it verifies signatures on its petitions; Change.org had not replied by the time of publication. By contrast, the UK Parliament petitions page is limited to UK residents and citizens, and requires a postcode for verification.
It goes on to discuss the implausible names used by some on-line signatories, the lack of geographical limitation for the petitioners (e.g. signatures from Spain or Germany were recorded on Change.org-hosted petition[s]), as well the promotion on social media of the "Rally for a Revote" campaign by accounts with pro-Kremlin profiles.