Adventures in the Mouse House

Does it matter if you read the books in order?

I started with Proven Guilty, even though it's quite far into the series, because it was the only one available at a branch of the library I could get to. I just wanted to read one to see if I was interested in the series or not. I thought it stood on its own really well.

I've since read the first three and just bought Summer Knight yesterday. I have also ordered Side Jobs from Amazon and pre-ordered the new one from Waterstones, which is out on the 28th.

Should I sit on Side Jobs and the new one, or can I dive in right after I finish Summer Knight?

For reference, I'm generally not hung up on reading things in the right order. I've spent most of my life depending on libraries, and it's only with the advent of online ordering that reading series in the correct order has even been possible. Unless there's great huge relevant gaps of plot missing, I really don't care about the minor stuff like characters' ages etc.

While I'm at it, same question re: Lindsey Davis' Falco series - my library has a lot of the later ones, and it's easier to get those first and then start ordering the rest.