What problems do nonsense suppressor tRNA create? What happens?

This results in continued elongation of a polypeptide past what would normally be one of the stop codons.

This will result in production of some nonfunctional or not very functional proteins.

But -- since the release factor is still recognizing the same stop codon, penetrance of your problematic nonsense suppressor isn't going to be 100%. Also note that there are two other different stop codons that are still good, and many genes have more than one stop codon in a row. The cell could still live, albeit less efficiently since it's wasting energy making functionless polypeptides occasionally.