So this alien super mutant is hiding out on Earth in human form. These are the things that make him different:
Shapeshifting takes too much effort for him to want to change to something different usually, so that won't cause any issue. Purple blood. No bones but can easily maintain having the appearance of normal joints and structure unless he's hit hard enough. Can generate electrical shocks; often involuntarily if he's been grabbed without warning. Fire breath. Invisibility, can still be seen on thermal sensors. Super strength and speed, includes abnormally high jumps. Higher durability. A colorful hat with a pocket dimension inside of it. Higher metabolism. Psychosis that increases as he goes too long without food before he goes on a carnivorous rampage. Regeneration; extensive damage causes him to shut down while he heals; He will be very hungry afterwards. Can climb anything. A strong aversion to medical environments and things. He likes to dig through dumpsters at night for food, especially on days when the stores throw out their expired food.
How much would he have to screw up before he gets their attention?
This isn't for trying to keep him out of trouble. He needs to accidentally find himself enough trouble that he decides to copy the ending of 'Dog With a Blog' and get himself on a talk show, reveal himself and his abilities to the public and thus him becoming a super powered celebrity will increase the likeliness of the military being unable to get him (because dangerous alien monster we fear because we don't understand) without the public being upset.