四个 si4ge5
六个 liu4ge4
嗯哼 en5heng1

I keep getting the tone wrong on ones like the above because it could be neutral and it could be something else but it seems whichever one I pick I get it wrong. I know there are other prompts where you can pick neutral or the right tone and you get it right anyways. Can more of these be added or is it absolutely imperative that you have the neutral or not the neutral?

In those cases (where I know the last character could be neutral or its original tone) I tend to correct my Skritter input right then if whichever I choose isn't correct (i.e. I mark it correct).

I never had a problem in speech with being understood using one tone or the other for the *last* syllable, so I don't feel the need to hammer myself that hard for it on Skritter - there's better things to focus on.

Some definitely have neutral tone though (for example 胳膊), the problem is that there are many ambiguous ones and some have different uses across China and also with Taiwan. It might also depend, among other things, where the word is used in the sentence or if you want to specifically stress that word. For example 势利 and 势力. I'm not sure TBH which one has 嗯哼 or even if it really matters :S. (According to my dictionary 势利 has although Skritter says otherwise.) Of course 眼睛 and 眼镜 are ones where it would be important to get the right one...maybe it would be most useful to have a list of ones which could be ambiguous instead of ones where it wouldn't affect understanding if mispronounced.

I don't think it's really a big deal, although it might sound strange to native speakers if you stress a word where it shouldn't be, since it's a kind of mispronunciation. Sadly, I can't think of a better solution than icebear's

Submit them as a reading correction when you see one that should have accept the neutral tone or the full tone and doesn't, and we may be able to either make it use a neutral tone or add it to this neutral tones exceptions list that we use for allowing the full tone for Taiwan-focused learners.