I haven't done any studies on this, nor do I know any, but I don't think it makes such a difference in practice. For any infectious disease to propagate, it needs to move from one host to another. There needs to be a "transit route". Now, usually diseases whose germs are excreted in the stool infect others orally (fecal-oral mode of transmission), so your germs somehow need to reach your own (auto-infection) or somebody else's mouth for a successful infection.
Now, aside from some (how to put this...) unsanitary sexual practices, it is not really the amount of germs left lying around your bottom after a "half-assed" cleaning session that's directly relevant for your infection risk. Rather, it's how much you get on your hands and fail to wash away.
In the case of Norovirus (one of the most infectious diarrhea agents), this is a real problem because the little buggers are very stable in the environment, and you need very few of them to get infected. A real risk here are instruments of normal social interaction -- handshakes, doorknobs etc. -- if you don't use very potent disinfectants for your hands after a bowel movement. Plus they spread via aerosols that permeate the air after a violent bowel movement or vomiting session.
Or, in the case of Cholera, it's a question of how many germs you get into your drinking water.
The fact that most civilized societies haven't died out from diarrhea appears to corroborate this - if anal hygiene was a relevant factor, we would have seen some differences here. In developing countries, people, especially children, die of diarrhea by the millions, not because they are not wiping their bottoms correctly, but because they have no access to clean water.
I just talked to the director of our university hospital's department of hygiene, and she was also unaware of any scientific studies about this question. She admitted that it would make for an interesting research project; writing the grant application alone sounds like fun. Might be a bit difficult to do a placebo-controlled, randomized, double-blind trial, though. In her opinion, wet naps (as long as they are made of a sturdy, poop-proof material) are probably your best bet.
This is a topic of great interest to backpackers. On a long backpacking trip without resupply, it becomes problematic to carry enough TP. You also have to deal with the used TP either by packing it back out or by burning it (and it's very hard to get it to burn 100%). "Backpacker's diarrhea" is extremely common[Zell 1993,Mueser 1997]. People used to blame such diarrhea on bugs such as Giardia in contaminated drinking water. This tends to be a contentious topic; I've written a longish article on it here http://www.lightandmatter.com/article/hiking_water.html . The references given in the article show that this is basically wrong. Backpackers probably typically get diarrhea either from pre-trip exposure or from hand-to-mouth contamination. Most people who get a bad case of non-wilderness-related diarrhea get it in contexts like public swimming pools, daycare centers, and salad bars. Some of this transmission, e.g., at the salad bar, is presumably from hand-to-mouth contamination. But in other cases, such a public swimming pools, it isn't. So the issue isn't just whether you can get your hands clean; it also makes a difference whether your dirty butt is contaminating water in which you swim or bathe. Some backpackers use natural materials such as rocks, leaves, or snow for wiping. Others advocate washing with soap and water. I'm not aware of any scientific evidence on the advantages or disadvantages of one or the other. I believe that auto-infection by hand to mouth is not actually common, because people's immune systems resist their own gut flora.
[Zell 1993] S.C. Zell and S.K. Sorenson, "Cyst acquisition rate for Giardia lamblia in backcountry travelers to Desolation Wilderness, Lake Tahoe," Wilderness and Environmental Medicine 4 (1993) 147, http://www.journals.elsevierhealth.com/periodicals/jwm/article/S0953-9859%2893%2971172-9/abstract
[Mueser 1997] - Roland Mueser, Long-Distance Hiking: Lessons from the Appalachian Trail, International Marine/Ragged Mountain Press, 1st edition, 1997, p. 96