I estimate that while most of my beliefs are true (otherwise I wouldn't believe them in the first place),
The former doesn't follow from the latter: it could be the case that each of your beliefs are your best guess, but you still give them a probability less than .5 if they contain more than a single bit of information.
I love seeing counter-evidence for everything. I estimate that while most of my beliefs are true (otherwise I wouldn't believe them in the first place), a small percentage is almost certainly completely false - and I don't really have any reliable way of telling the two apart.
Indiscriminatingly looking for counter-evidence for all of them can be very rewarding - the ones that are true are much more likely to sustain the assault of it than the ones that aren't. Yes, I might ignore counter-evidence of something that's false, or accept it for something that's true, ending up worse off, but it seems plausible that on average it should improve quality of my beliefs.
For example some of the standard beliefs about human sociobiology that seemed to be extremely widely held here are:
Charting Parenthood: Statistical Portrait of Fathers and Mothers in America disagrees with them.
These are not direct tests of sociobiological claims, so what we have is not exactly what we would like to, but I find them to be quite convincing counter-evidence. My belief in these sociobiological claims is definitely lower than before, at least as far as they concern modern world, even though I can imagine more focused studies changing my mind back.
More counter-evidence for things we commonly believe here, sociobiological or otherwise, welcomed in comments.