OK, let's try to describe the performance problems more precisely.
For me, performance problems fall into three specific cases:
1. dropped keyboard input
2. slow update of game UI
3. slow server round-trips
1. Dropped keyboard input: this is in some ways the most annoying. For me, this happens most commonly when trying to type in chat. I don't know whether this is a bug in Flash or a design flaw in the game, but it is extremely annoying. (I suspect that the system is polling for keyboard input instead of using an input queue, which causes keystrokes to be lost if busy doing something else.)
2. Slow update of game UI: periodically, the game will "freeze" and I can hear the computer fans come on. This is the lesser problem in my opinion, except when trying to play a mini-game or other instance which requires active control and fast response (smuggling quest, A Summer's Day, etc).
I believe these are both caused by high CPU demand of the Flash client. (An older machine with 16Gb of memory performs significantly worse than a newer machine with 8Gb, both with the same wired broadband Internet connection, browser and Flash version.)
3. Slow server round-trips: sometimes actions which require server interactions hang for long periods (5s+). For example, selecting an animal or resource node doesn't bring up the menu quickly. Usually, cancelling and retrying fixes it, but sometimes things remain slow for 10s or so. (Apparently, some of the game servers are regularly overloaded or unavailable.)
I'm on Mac OS X (Lion), using the Chrome browser.
If you experience performance problems, please try to list what happens as explicitly as possible so we can help TS focus their performance tuning efforts.