Are their pitfalls?
If I just tell another registrar to transfer the domain, is that all there is to it, or will Verisign block or bungle the move?
And finally, will this screw up the search engines trying to find my site?
Once you've initiated the intra-registrar transfer, the gaining registrar will send an e-mail to you as the admin contact & request confirmation of the transfer. Once approved, the losing registrar (NetSol/Verisign) will send another mail requesting you to confirm the transfer. The format of this mail will be a little dubious and will have "information about your account" as the title line. Follow the link in the mail & you'll get to confirm the transfer again.
Few more days & all will be calm & you'll have a nice new registrar. As far as s/engines go, you shouldn't encounter any problems if you're merely transferring to another registrar as the nameservers won't change. If you do end up with different nameservers, I'm not sure if there'll be any consequences on the s/engine front - maybe someone else knows about this.