I pretty much agree with everything Jim's said (thanks!), but it's also possible that this could be something other than a firmware issue. Given that you've got 5.3 MB available (and that free memory isn't as big an issue on the Treo 650 as it is on earlier models anyway) it's probably not a memory problem, but there are some other possibilities to think about.
For one thing, how did you go about setting up your Treo 650? Did you simply HotSync it with your PC and select the same username that you were using on your old Palm? If so, that could actually cause a lot of problems right there, because some of the backed-up data files from your old Palm could be conflicting with your Treo.
So I'd recommend that you hard reset your Treo (hold down the power button while pressing in the reset pin - this will erase all of its memory), then go to your Palm Desktop backup folder (c:\program files\palmOne\(your username)\Backup) and rename that folder to "Old Backup" or something similar. (anything except "Backup", basically) Then, HotSync your Treo with your PC, select that same username again, and reinstall PlecoDict. Assuming PlecoDict now works correctly, you can then proceed to reinstall any other software you were running before. You can go into that "Old Backup" folder if you need to reinstall any data files or programs that you no longer have separate copies of, but be very careful to install only software that you actually recognize, so that you won't accidentally reinstall whatever file was causing the problem.
Following that procedure should eliminate just about any potential cause of problems, so if PlecoDict still crashes after doing this then there may be something wrong with your Treo (perhaps a defective flash memory chip or something along those lines). But I'd say it's at least 90% certain that a reset and reinstall will fix this.