I can paste cards into the maindeck on here, but not the sideboard. It's really annoying.

I believe you can actually paste cards into the sideboard as well by preceding sideboard cards with "sideboard:" in the mass card entry field. To be honest, I realized this functionality by mistake when copying a decklist. Example:

4 Lightning Bolt
4 Delver of Secrets
4 Preordain

Sideboard:
3 Dispel
3 Electrickery

Yeah, that works. Thanks a ton.