Overall, this is a great episode, but not one of the best of the first season. By now, Columbo's character and methods are firmly-established, so it's up to the writers and other actors to play off of him to make an episode shine. In this case, the actors do a decent job, but the writers somewhat let us down.
The peformances are overall quite good, with the best showing from Janis Paige as Goldie. Of course, Peter Falk was brilliant as usual. Patrick O'Neal as Markham was a rather run-of-the-mill villian. I didn't think the character was smart enough to make him interesting and O'Neal did not really add anything beyond what the writers had given him to flesh the character out more. Columbo decides he has fingered the killer early on, when he finds Bo Willliamson's car tuned to a classical music station, given that Bo only listened to country music. It just takes some cat and mouse with Markham, waiting for him to make a mistake before Columbo can arrest him. However, this one large and rather glaring mistake is really not all it takes to catch a killer. Markham practically dares Columbo to dig up the contstruction site, so we know the body is not there, despite all the hints he gives in his lectures about Egyptians and tombs. Had Markham already disposed of the body somewhere else, Columbo's whole plan would have been ruined and he would have had no evidence to catch Markham. It's hard to believe that Markham is so foolish as to try to get rid of Bo's body right after Columbo's fruitless search of the pile. Of course, Columbo was going to be following him around waiting for him to make a move. A smarter man would have led Columbo in the dance but had a completely different location picked out and waited for the heat to die down a bit.