The apartment smells horrible due to the tenant allowing her pets to urinate all over the place.

Have you heard on the BP podcasts when certain guests walk into a place and the stench of cat urine bowls you over? 

This may sound like you are creating a hurtle for yourself, but in the end honesty is always appreciated and allows for a much smoother transaction. - My advice though is to make sure your numbers are tight and make sure you can successfully dispo the deal!

Then bugs started crawling out of it and when heated up smelled like urine.

I have even had several friends who have gotten rid of cats due to urine issues and that is why half the cats end up in a shelter. 

The major hurtle for a 1031 Exchange is the timelines, however if prepared, you can easily be prepared and they do not become an issue.  

Our company in addition does remodeling projects for clients and we come across cat urine, smoking, pets smells, mold etc.

Most tenants who have dogs (I say most because there are some that do not fall into this category) do not take care of the property as if it were their own and when you add a pet dog (or dogs) in that equation things are dirtier because of the dog feces and urine, the dog tearing things up (scratching doors and walls) and the annoyance of leaving the dog alone and it barking constantly affecting the neighbors (this is more of an issue with apartments not houses).

The unit has a heavy cat urine smell.

Both units right now have pets in them, and I didn't discover any urine smells, but it wouldn't surprise me if there are some hidden smells or damage that I didn't catch during the inspection.