Don't use SHA-1 please.
There's no good reason not to use a secure hash function.
I'm not sure why they haven't retroactively calculated checksums for older versions.
But you're right that SHA-1 needs to stop being used: https://sites.google.com/site/itstheshappening/
These researchers have found the first "freestart" collision, and they estimate the SHA-1 collision cost to take a few months, costing between 75K$ and 120K$.
Practically speaking, I don't think anyone could make a profit by forging a Handbrake release, but the FBI probably do have some very high-profile targets who use video encoding software.