Writing that title hurt. Reading it while I’m writing this hurts. But in a bizarre way, spelling/grammar both are and aren’t important. Let me explain…
When they ARE important:
Anything that is either sent out formally or represents you online. Certainly your CV, any letters/e-mails you send (particularly speculative ones) and job applications need to be spot on. These details count. If the choice is between you and your identical twin and one of you spelled the company name wrong, that twin is still job hunting. This is especially true for anyone trying copywriting or proofreading as a job.
When they AREN’T important:
Anything that is for your benefit alone or, at a push, informal notes to people you know well. If you’re on a roll, bashing out page after page of script or story then don’t stop to check your spelling. Take advantage of the inspiration while it’s there instead of risking it getting bogged down in there/their/they’re. You can return and deal with them later.