FACTS:

He obviously saw the cider the night before Haynes was murdered (actually it was the morning of)
He had to be standing in a specific spot
He only could have seen the cider between 615-625 AM
There was an argument that was overheard by the iron maiden (Miss Brady)

A good defense lawyer could argue every point in a courtroom. So would he be convicted? It is a gray area to me.

He confessed.
As with many episodes, there is no "arrest".

He told Columbo that he did it and he'd do it again, so yeah, he's going to jail. There are a lot of cases that will get a conviction due to either the evidence or they confess, but there also a few that a good lawyer will get the murderer off.

Rumford's mistake WAS confessing. If he hadn't, it would have been a tough conviction.