While you can get by with that side panel for some time, it's HIGHLY RECOMMENDED to replace (or at the very least, repair) the case for the long run.
The biggest concerns will be cooling (as the missing panel will negatively affect the current system) & the potential of dust & other debris getting into your system components.
For cooling, try to keep the room a bit cooler... if possible (but above the dew point, as you DON'T want condensation) to compensate. You may take the "redneck" approach by slapping a box fan on the side to try & help with cooling. Just make sure you know which direction of the air flow in your system & if your system runs on a positive (pushing air out passively), negative (pulling air in passively) or balanced air pressure. The extra fan may not run as fast or as well as the built-in ones for your system, but it should help to some degree.
As for dust & debris, this is more of a monitoring situation. Just keep pets & other loose stuff away from the system (as computers tend to naturally draw that stuff in like a magnet).
I hope this helps in the short term.