Ward's shoes were an important clue because the killer was very short, possibly a woman, while Ward Fowler was average height for a man. However, Ward wore special shoes with heel lifts that made him appear a few inches taller. When Columbo noticed these shoes, he realized that Ward was the same height as the killer. I know that Columbo saw Ward every day, but Ward presumably had heel lifts and pants to cover the shoes. Only an observant person would notice (like Columbo). Or Tony, the guy from the deli.

Regarding silver certificates, they are a form of investment. when you purchase gold or silver, you have to store the metals. They are heavy, you need space for them, you have to secure that space, etc. However, you can bypass the inconvenience of keeping precious metals by allowing the issuing bank to keep them in their vault. That way, the metals are protected and insured.
Any time you want access, you show your certificate and redeem the value of the silver.

An IOU is exactly what you assumed. It sounds like "I Owe You".

Regarding the chances that Claire would be at Tony's (He's the guy who owns the Deli), she apparently went there quite often.

I thought two things were bizarre with the "expert marksman" scene. First, Columbo asks for help and, I paraphrase:

Columbo: What do you think?
Ward: I think I'd better try and help you. Because you're going to ask me to, aren't you?
C: Oh Boy, you did it again Sir, you read my mind, would you?

And later, Ward says "IF the killer was an expert marksman", and he explains that part of being an expert is to hit moving targets. Like a woman running. Like Claire (unlike Tony, the guy from the deli). So what was his point?

Ward's initial reaction was ridiculous. He kicks out his "gofor" for "trying to give me an alibi" and then says: "Well, if he says I was, then I guess I was watching the game with him". So why get angry before? And like Matti says, how could he have forgotten so fast? "Poor Claire murdered and God knows what I was doing or where I was". A true ham of the first order.

There is a difference between kill and murder. Murder is illegal. However, the way the words were used in this context was if the robbery was a cover to eliminate Claire, she was murdered. Of course either way she was murdered (and killed), but it's first degree murder if it was planned in advance.

I wanted to clarify my paraphrasing above when Columbo is amazed that Ward read his mind:

Columbo: What do you think, Mr. Fowler? Could you help me with this?
Ward: I think I'd better try and help you. Because you're going to ask me to, aren't you?
Columbo: Oh Boy, you did it again Sir, you read my mind, would you? Imagine the great Lt. Lucerne, etc.

Fowler didn't read Columbo's mind, Columbo asked him for help. If anybody else had a different interpretation of that and the "Expert Marksman" theory, I'd love to hear your thoughts. An expert marksman has to hit a moving target. Proving....what exactly?

One for me would be Doris Buckner. Not because she "bent over backwards to spoil Rodger" and this is where it got her, but just for general reasons.

I've mentioned it before, but one clever things about Lady In Waiting is how Mrs. Chadwick and Peter Hamilton both end up disillusioned about Beth. Even though Columbo already spells things out to Peter before he confronts Beth, it would be interesting to see their reactions.

I'm sorry, I put that in the wrong thread. It was meant for the "Reactions" thread, of course.