If I use Apache & ngnix together will I have fewer problems?

If I use Apache & ngnix together will I have fewer problems?

Yes, of course.

Please be sure to install and setup mod_rpaf in Apache, if you are going to setup Nginx as reverse proxy to Apache.

I was wondering if I used Apache and Nginx together, with nginx
serving static files, apache php would I get both performance and
compatibility?

Performance is purely based how you configure these. Your site will, of course, be more compatible (for plugins).