What are all the main problems that can occur when the spark plugs are gapped to far apart?

 

The spark will be hotter. This can cause "spark knock".

Larger gap requires more spark. More pressure in the cyclinders requires more spark. So you may see a spark failure (a miss) when under load.

Last, if it was way out your plug could hit your piston,

 

How many thousandths apart past the right gap would it take to hit the piston?

 

That depends on a great many things like, Piston shape, head design, even the type of plug. Many race type motors have very little clearance between the piston and the head and some of the high reving drag cars need .100 or more clearance because things tend to strech at the higher RPMs.