Just to update. Today I completely restored the OS 3.2. i.e. I connected the iPad to iTunes and clicked RESTORE, and it downloaded the OS and reinstalled the iPad from scratch. After that, I've been able to auto-connect to my Time Capsule N. Hopefully it stays this way. I can also turn WiFi off and on in the Settings menu, and it immediately connects to my network without me having to tap it.
ALSO, I am now able to connect to public WiFi network (one that requires you login). Before then, it just told me "Safari can't connect because you've got no Internet connection" (or whatever it says to that effect). After the restore, it works like it does on my iPhone.
So, for those with the above issue, RESTORE your iPad! Not sure why it shipped this way, but it seems this fixes it!
However, still 39mbit on wireless N, bizarrely, which I'm pretty sure is Apple's doing.