UHC CEO Murder Suspect Made Sloppy Mistakes, Says Ex-FBI Profiler

A former top FBI profiler is breaking down Luigi Mangione’s arrest today -- the prime person of interest in the murder of UnitedHealthcare CEO Brian Thompson  ... and he's also pointing out all the "sloppy" blunders made along the way by the person who did the shooting -- Mangione has not been charged in the case.

James Fitzgerald, an ex-FBI profiler who served in NYC during the late '80s and '90s, tells TMZ that the alleged killer -- who he makes clear is innocent until proven guilty -- was no criminal mastermind ... he was just someone laser-focused on completing a mission.

Fitzgerald didn’t hold back, calling out the missteps of whoever committed the murder -- like the "amateur" bullet engravings, using the wrong kind of firearm -- and he comments on key evidence allegedly found in Mangione's possession, asking why it wasn't ditched.

He also says it makes zero sense to keep the gun and manifesto in one's possession ... even if the person of interest was bracing for a hypothetical shootout, because the weapon he used wasn’t exactly built for a blazing gun battle.

As for Mangione's public Altoona, PA McDonald’s sighting, where he was eventually recognized ... it's another move that screams amateur, Fitzgerald tells us.

All in all, Fitzgerald breaks it down for us, making one thing clear -- there are a lot of missing pieces in this puzzle.

Watch "TMZ Live" today ... check your local listings.