I was having issues using the built in Swype with any browser under JB. Fixed it by disabling the built in and installing the beta from their site.
I've had no problems with Swype on JB but have a weird issue within Gallery where every time I tap on a folder that has all my pics from my Camera app (pre-JB) the Gallery app just closes! Gotta' love updates, huh?
After the update I have several issues that are driving me nuts.
Missing texts messages
Sleep Mode gone
Auto space with browser not working
Gallery pics all disorganized
Phone and People apps not organized. Many duplicates and "(no name)" entries
Speed dial settings gone
Emergency contacts gone
Contact icons missing
Just to name a few.
Yes hitting the button lower left on phone, brings up a menus no exit. Have to go to top right of screen, and scroll down a bit click icon to exit. Plus gallery not sinc to Facebook. No weather app.
My Swype (paid) and gallery are working fine under JB. I did do a factory data reset and re-rooted using the Ubuntu exploit. An fdr is recommended by some prominent posters, not that makes it true. But I'm very happy with my results.