Yes, these are risks to be sure, but what's unclear to me is how great a risk they might be. According to two different studies I found, a 325mg/day dosage leads to a 3 to 4 times greater risk of upper gastrointestinal bleeding (UGIB) than no aspirin. However, I don't see numbers for the absolute risk (e.g. incidence per thousand). According to the Nurses' Drug Guide, UGIB is a serious possible side effect, but not a common one.
To make it more interesting, another study I came across found that the risk of UGIB was highest in those taking it for a week or two, and lower for longer-term use. This would seem to indicate that many people who are going to experience UGIB do so rather soon after starting it.
I haven't dug into the numbers on renal failure yet, but what I've seen so far still gives me pause. At the same time, I'm still not entirely convinced the risks outweigh the benefits, especially for someone like me who also has a predisposition to heart disease (hypertension and high cholesterol) and might benefit in that way as well.