When I run the app locally I get this error "The resource from “http://localhost:4502/content/dam/path/to/script/file.js” was blocked due to MIME type (“text/html”) mismatch (X-Content-Type-Options: nosniff).
This works in production but I've got no idea how this was achieved.
With this reason, few possible routes to narrow down the issue(as the issue is only with your local and not in PROD),
Compare the network calls (filter requests to "JS") in both local and PROD in same browser. (two different tab)
X-Content-Type-Options:nosniff on Response Headers in both local and PROD
Confirm if the JS file that you are checking is same in both local and PROD.
Can cross verify the asset "Properties" from being in DAM. In particular, "Type" property
Look for OSGI configuration related to MIME type in both local and PROD. There exist a config named "Day CQ DAM Mime Type Service" in 6.5.0. Not sure of its equivalent from 6.1 (Should be available in the same name. Else, do search for MIME type and locate the one related to DAM)