Are Lawful Interception Features considered "flaws" or "backdoors"?
Many developers and organizations include flaws quite consciously to allow government intelligence and law enforcement as well as other purported stakeholders (usually copyright and software-patent vigilantes) multiple layers of to access end-user systems.
There is a misclassification here. To describe deliberate law-enforcement features, openly developed to meet legally-imposed requirements, as "flaws" does a disservice to the developers involved.
In the United States, the Communications Assistance for Law Enforcement Act of 1994 legally requires telecommunication carriers, manufacturers of telecommunications transmission or switching equipment and providers of telecommunications support services to co-operate with lawful interception of communications.
Any such requirements can only increase the "surface area" involved for vulnerabilities, but it is cynical to assume that they are necessarily exploited in all cases.
Have there been any deliberate backdoors?
Yes, there have been plenty of instances of deliberate backdoors discovered.
Here are a few examples:
Static Detection of Application Backdoors, Chris Wysopal, Chris Eng, Veracode, Inc.
Borland Interbase 4.0, 5.0, 6.0 was discovered to have a special credential backdoor in 2001 shortly after the software was open sourced. The special credentials, username “politically” and password “correct”, were inserted into the credential table at program startup. The support for user defined functions in the software equated this backdoor access with system access. The backdoor went undetected for seven years.
Attempted backdoor into Linux discovered
Backdoor(s) in HAL BBS for the Commodore 64 (Caution: self-citing.)
GSM Network encryption deliberately easy to break [Ref: 1, 2] All of this is apart from the fact that, once out of air, most telephony networks even work without encryption. See, for example, this report on wiretapping:
Since 2002, the annual wiretap report has included a curious statistic: the number of times law enforcement encountered encryption on an authorized tap, along with the number of times that this prevented them from getting the evidence they were seeking.
But not so fast: the latest wiretap report identifies a total of just six (out of 3194) cases in which encryption was encountered, and that prevented recovery of evidence a grand total of ... (drumroll) ... zero times. Not once. Previous wiretap reports have indicated similarly minuscule numbers.
Routers seem to have lots of them, both home routers and enterprise routers. They appear to be a favourite amongst intelligence agencies because a compromised router is a gateway into the traffic on an internal trusted network, which is often not encrypted. The Juniper Firewall back door was particularly sinister because it involved the choice of "Q" value in an encryption scheme promoted by the NSA. In effect Q is a secret key for the entire encryption scheme, so to exploit it you would also need the ability to intercept the encrypted traffic.
Please add any additional examples here
If your answer is merely another example of a backdoor, please add it to this answer rather than hiding other approaches in the noise. This answer has been marked Community Wiki; I am not getting any reputation for it.