There are a few security issues I can think of.
Replay and substitution
There is nothing preventing a man in the middle from replacing a signed resource with another signed resource (captured previously). For example, I might be able to make a green GO button appear where a STOP button should be, causing you to drive off a cliff. Or I could make it look like your cash transfer failed so that you submit it again and again and I get paid multiple times.
I could intercept your request for an image and reply with a 302 redirect to a URL whose querystring parameters comprise a XSRF attack.
Loss of privacy
A hacker monitoring your traffic may be able to determine what pages you are visiting by examining the pattern of http requests for static resources.
DoS via cache poisoning
A hacker, working a man in the middle, substitutes an invalid file for one of the responses. The proxy caches the file. Browsers attempting to use the cached resource will find that it fails validation and will display an error, with no easy means of bypassing the problem.
P.S. Performance issue
Also, there is a performance issue-- resources that are subject to a checksum will not be able to be progressively rendered, because the entire BLOB is required to compute the checksum. So your images will appear slower and your movie won't start until the whole thing has made it through the pipe.