Sometimes when I'm going through a list of words and I don't know which tone a certain character is, I click on the "listen" button to hear it and then I put in 1st, 2nd, 3rd, 4th or neutral tone bases on what I hear. I usually get the right tone if I listen to it first. After inputting the tone, I sometimes mark the character with a red check mark , for "wrong", so that it comes up again soon, but sometimes I get lazy and I don't do that and just move on from there to the next word in the list.

My question is, should I be marking all of those characters as "wrong" before moving on, or should I just move on because they'll probably come up again later (when I'm cramming a list) ?

I mark things wrong when I use any kind of hint (mnemonics etc.) It seems to work out better in the long run if you're strict on yourself.