There are no serious problems that you will be guaranteed to run into if you don't install the patch, but several that you may encounter. For example, at the start of act 2 in an unpatched game you can find your own way off an island, rather than rescue an imp to show you the way, and thus miss out on a cut scene, causing very serious problems later.
Despite the removal of several exploits, I would still install the patch for the various fixes and enhancements. There are still ways to cheat, if you wish to do so;
For you cheaters out there (The Duplication Trick)Hex editing - gold, experience, stat/skill points 
