Dialer app becoming too slow and less responsive
This is likely a combination of two things: a) stuff that the dialer has to load on startup and b) possibly shortage of memory (RAM) created by loading those things. The biggest gains are to be had by resolving (a) however, this will also have the side effect of resolving (b)

You might like to try clearing the following:


Call log - this is loaded each time the dialer is loaded.
SMS messages - Some users have reported that a large number of SMS messages can cause the dialer to slow down, though I'm sceptical that this makes a difference.
Contacts - finally, the number of contacts does have a bearing. Not only the ones you can see ("My Contacts"), but anyone you've ever emailed (i.e. Other contacts in GMail contacts).


The last point can be quite important. I have about 130 'real' contacts but nearly 1000 people I've emailed at some point while using GMail. There were all being synced to my phone, just not always shown.

It is important to make the distinction between RAM and persistent storage. For example, clearing out your trash, deleting emails, uninstalling unused apps, or moving them to SD storage is unlikely to help, because these are using up persistent storage, not transient RAM. 

Having lots of persistence storage free means just that apps can't use it to run any faster. RAM, however, can make them fly.

You might also like to take a look at Superdial and Dialer One, two dialers that I've found most agreeable. They also have T9 contact lookup, which can be a dream to use.