“What else can go wrong today?”
You're having a bad day. You are at home with your husband. While you're writing a document on your computer, the program crashes and you lose all the work you've done. You make this complaint.
What else can go wrong today?
"Else" means "other things". It's often used with questions:
Who else is coming?
We should definitely go. When else will we get a chance to visit Spain?
"What else" means "what other things". You start a question with "what else" when you have some examples of things, but you want more:
What else should we bring?
What else can I say? I've already apologized multiple times.
When a plan, an action, or a situation "goes wrong", it means that there are problems:
What went wrong at your birthday party?
If anything goes wrong, call me immediately.
When an object, like a car or a toilet, has problems, you don't say that it "went wrong". Instead you say "it's messed up", "it broke", "it has problems", etc.:
The hood of my car is kind of messed up.
My laptop broke last week. I have to get a new one.
When a lot of things have gone wrong in a day or a short period of time, and then you find out about another problem, you say:
What else can go wrong?
This is a way of complaining about the number of problems.
The stress in this sentence is on the word "else".