Sure, you might be able to check that it's not phoning home to some server somewhere with the generated private keys, but you'd have to be an experienced cryptographer to check for more advanced vulnerabilities.
Indeed, it's possible to use the mouse movements to do something deterministic or something. I did not go to great length to establish the integrity of the code, so I may have overlooked something - it's 4000 lines, after all.
But the brain wallet is straightforward: It's private key is SHA256(Passphrase) and the SHA256 code does just that: It creates a sha256 hash. And that is a very small amount of code. You can create it with JS and verify that on the command line:
$ printf 'my really diffficult Paßphrase (made from P. Cubensis and A. Uigedail)' | sha256sum
That said: I obviously don't guarantee anything.