Actually, this is a fascinating phenomenon. The problem is, 't' and 'd' are not always as distinct as we'd like to think. There's a whole range of sound in between the two. In response to the original question, there is something funny that happens with 't' begins an unstressed part of the word, as in 'mister'. If you listen carefully, most Americans will not actually pronounce it with a strong 't' (unless they're trying to be formal or speaking slowly). Neither is it 'misder', though. What happens is something like 'mis (pause) der' instead, with a very short (but definite) pause and a very light 'd'. In addition, the unstressed part of the word ('ter') will typically drop in pitch compared to the stressed part.
It's hard to describe this exactly, but listen for it and you'll notice it. You're not likely to find this described in any textbooks as it's quite subtle. This phenomenon is even more pronounced with 'nt' combinations. For instance, 'dentist' is often pronounced as 'den (pause) dist', with a very light d. 'den tist' with a strong t will make you sound British or very formal. (There's also 'denist', of course, an informal/regional version). "Isn't it?" becomes "Isn (pause) dit?", again with a light d. In other examples "after" becomes "af (pause) der", "faster" becomes "fas (pause) der" etc. That small pause and drop in pitch are very important, by the way - saying 'afder' and 'fasder' and 'dendist' won't sound right at all.
Not using phonetic transcription here, but I hope you get what I mean. Listen for it and you'll notice Americans do this.