Just consider his methods of "solving" crimes:
- Get called out to murder.
- Meet someone at the crime scene.
- Decide they’re guilty.
- Repeatedly harass them.
- Ignore all other leads.
- Harass the target some more.
- Evidence against the supposed killer magically turns up.
Abandoning all other lines of inquiry is an act of gross negligence and must lead to many killers going free.
No you may argue that Colombo always gets the right person however we only have the confession (false confessions are a well known result of psychological torture) and the television's word that he did. What about all the investigations Colombo must have bungled but never made it to air?
Yes mourn the man who played Colombo but also mourn the hypothetical and fictional men and women who've hypothetically spent decades in an imaginary prison for crimes that they did not commit.