I have discovered what I believe to be a bug.
I have not tested this with every key but I do know of a couple that this problem occurs with. Having Scroll Lock or Pause set as my PTT key, I was able to replicate this bug 100% of the time.
1. Hold down the PTT key (In this case Scroll Lock or Pause)
2. Hold down the Ctrl key
3. Release the PTT key
4. Release the Ctrl key
This will cause the Teamspeak client to think the PTT key is still held down, even though it is not. Tapping the PTT key will reset it. Surprisingly this happens to me a lot on accident, and it is rather annoying because I do not realize it until someone tells me my mic is open.
I have not tested every key, but I do know that the problem does not occur with every key. Letters and F keys seem to work without any issues. I have also tested this with both the 32-bit and 64-bit clients and have tried changing the input method from Default to Keyboard and Mouse Only, and to no avail.
I realize that I can just change my PTT key to a key that works right, and that is what I will do for now. I prefer to use Scroll Lock because it tends to not interfere with anything in most of the games I play.