Do you have any idea of how high is the percentage of discarded transations under "normal" conditions?
I'm not sure what "normal" conditions are. If you mean no-one-trying-to-abuse-anything situation, then 0%. Not that every single modified txid would be an attempt to abuse, but there doesn't seem to be any good reason for doing it and certainly none of the major clients support it.
Would it be feasible for some miners to be logging those "incidents"?
Yes. In fact, you wouldn't even need to be a miner. Anyone relaying transactions (e.g. running the full bitcoin client) could, in theory, log these "incidents".
Someone actually did this to an extent after mtgox made their initial announcement. From the results he posted to this forum, probably only "counts" were logged (not each individual transaction). Their count was generally quite low, with a few spikes here and there (and a 24 hour break on Chinese New Year, if I recall correctly).