Should I be concerned about a ceiling light fixture that was installed without the mounting bracket?
Mounting brackets for all light fixtures I’ve ever dealt with are fairly simple. There are some variations but they accomplish the same purpose: they are secured to the box and then have either a couple of screws (common for wall-mounted fixtures like sconces) or a lamp nipple (common for ceiling-mounted fixtures) that secure the actual fixture or fixture chain to the box. Some use both screws and a nipple. It’s a fairly standard affair once you have the right screws, even if they’re not the originals. The contractor would have used his own brackets and screws.
In short, I wouldn’t be concerned unless you have reason to believe the contractor is unqualified.