1) I mark 100% of the emails from a particular sender or with a particular subject line as junk, yet the junk classifier still puts emails from that sender or with that subject in my inbox. This is the low-hanging fruit -- the stuff that is so obvious that it is spam that a human can figure it out without looking at the message body at all, yet Thunderbird can't seem to get it right no matter how much you train it. I can only guess that they are placing too much weight on the body content (which is easily padded with hidden text to con the algorithm) when a bad sender/subject should trump whatever is in the body.
2) Emails from people that I've emailed in the past sometimes end up in the junk folder. I thought they were supposed to be whitelisted automatically (by automatically being appended to some special section of your address book).
3) I've implemented message filters to detect certain words like our product name and move the incoming message to a high-priority folder, yet messages that should match the filter still end up in the junk folder on rare occasions (and, yes, I have it configured to run the filter before junk classification is applied -- I'm assuming that junk classification should not be applied if a filter moves the message out of the inbox).
4) It sometimes seems to just stop learning, so I have to reset and retrain the junk classifier or it gets to the point where the only emails that it recognizes as being junk are the ones in a foreign language.