a little bit of clipping on anologue equipment is aight because of its "soft clip" nature where it naturally rounds off distortion giving it a pleaseing sound.
clipping in digital land however is another story. mixes should never exceed 0dBFS. if your clip indicator is lighting up, you are getting distrotion, whether you can hear it or not. if you turn your monitor level up louder you probably would hear it but the point is that if the clip light is lighting up, the distortion is there.
if you want your mix to sound as clean as possible, dont let it clip. simple as that.
if its your drums that are causing the clipping, compress them.
i would not recommend compressing everything in your mix. this will squeeze the life out of your mix. why would you want to compress anything that isnt even getting close to clipping anyway?
firstly, get your whole mix balanced so all the sounds are the correct volume in relation to each other. make sure nothing is clipping. if the clip light is lighting up, pull down the master fader. then what you want to do is find out the peak dB level of all the individual tracks in your mix (play each track right through). the bass peak level may be at -5dB and the piano peak level may be at -3dB and the drums peak level may be at -0.5 dB. in this case, compress the drums (since they are closest to clipping) and then raise the overall level of the entire mix. the next thing to clip will obviously be the piano. so you may need to compress that too. but dont compress unless its neccessary. use released albums as reference material and if your shit is competing with those albums volume wise you dont need to compress any more.