@all: thanks a lot for your feedback! It's good to see that so many people care about security. To quickly summarize your questions: We are using the secure CBC mode and have always used it ;) You can have a look on the source code directly on the website (because it's all client side JavaScript), but some parts of it are minified. We are working on a detailed description of the technology behind InstantCryptor and will publish it soon via Twitter (@cloudrail). If you are interested in the technology to easily add cloud storage into your application visit cloudrail.com to get a free copy.
I don't know that I'd necessary push for ChaCha20, but lack of ciphertext authentication is a clear problem. AES-GCM or even AES-CBC with an HMAC that's validated prior to decryption can provide the needed authenticity checks.