I put a custom object into a managed package, and installed that package into another organization. I can see the custom object in the interface just fine - it shows up under the managed package area, and I can write reports against it, but I'm getting 404s on hitting the REST API for it. I am checking that the namespace is correct. What else should I be looking at? Object permissions? API permissions?
When you install a managed package in an org, you have to be sure to choose "Available to all users" in order for everyone to have access to custom objects within it.
Your options now are to either remove and re-install the package selecting this option (the easy way!), or to create custom profiles and reassign all of the users who need access to the new profiles.
One other side note, even when you do have access, remember that you'll need to use the package namespace prefix to access the objects as well.