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Not really. The only issue will be opening the files. You'll have to remember to tell the file which app you want it opened in.
 
If I remember rightly, Adobe say that you shouldn't have multiple copies on one Mac. I can't remember where I read that, it was some time ago. Having said that, I've always ignored their advice. I have CS5, CS6 and CC installed on my Mac and all run fine.

The only issues I've had is running AppleScripts - sometimes the script will launch the wrong app. I think that's more a case of the script assuming only one copy of Illustrator is installed though.
 
Same here. Running CS5.5 (Acrobat X, Illustrator, Phoshop and InDesign) and CS6 (InDesign).

No problems here.
 
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