With the new item shop, my game freezes for a short peroid (usually less than a second) when:

-Opening the shop
-Purchasing an item
-Using one of the filter buttons (though this freeze is very short)

It is quite annoying.

The old shop would only freeze the first time it was opened during the game.

Same.
I don't know if it's due to my hard drive or something, but my League of Legends is installed on a 7200RPM hard drive with a SATA 3 connection so it really shouldn't be slow. I probably should buy an SSD if that is the problem.
I'm also running an AMD FX 8350 overclocked to 4.8 and a GTX 660, so my system spec really isn't a problem.

A friend and I are having the same issue.

It's not that bad, but it's not something I want.
The new UI is really laggy in general. I have to close more than usual to get 60 FPS. I'm probably not going to be able to stream like this.