From the guidelines...
13. Skip is a great option
If for whatever reason you don't want to vote on this case (but you want to continue voting on cases), feel free to skip the case. It won't count toward your cases reviewed today, and the case will still be high in the queue for other Tribunal members to vote on.

This is suppose to be the rule but just now I skipped some cases and when I went to punish my first troll it said I was past my 3 per day limit.

Has this happened to anyone else?

This has happened to me.
Riot MAKE UP YOUR MIND!!!!!

why did you skip 3 cases

Yes, this happens, and shouldn't happen.

EDIT: I skipped a case because it did that thing where the summoner name didn't show, the scores didn't show... basically nothing showed. I had to skip it because there was no way I could properly judge it.

They stated that they do not want you to keep skipping cases until you find an obvious one so right now they are counting toward your limits.

The limits will be raised "soon" but there will always be a limit.

A few time web wasnt loading full information. I did try refresh. I skipped, and the same prob as OP.

The same thing happened to me when I skipped my last one today as it was continuously blank except for the reports and the player's name. I just took the link back to the tribunal and could review cases again; unfortunately, it just kept giving me the same bugged case.

When the reports are bugged they should not count towards the limit for the day. Good to know others have the same problem.

Yeah, additional confirmation for this issue.

I am very sad now. i was being very helpful reading every single detail until i clicked skip. now i will not get any ip points for my efforts. i am so sad now. i read the policy saying skipping is allowed and will not count against you. now i lose out on so much ip points, now i dont know if i want to help or play any more.