My computer has a USB port that appears to be too loose, with attached devices exhibiting too much play where the USB plug is inserted into the port. The port still works, as devices continue to communicate correctly when attached to this port. The port itself is tightly attached to the computer chassis. Should I attempt to tighten the port? Is it at risk of eventually failing?
I would say most likely no. If the physical housing is still soundly attached to the case as your description sounds like. Then the only thing I think of is that the center plastic tab that holds the metal connectors is missing/broken. If it is missing that ports effectively dead you will need to either replace the part that the usb is attached to [daughter card or system board depending on model].
If you happen to still have the plastic tab or it hasn't fallen out yet it MIGHT be possible to glue it in place again but the chances of getting a perfect fit like is needed are low.
If you continue to use it with no plastic tab to keep the pins straight they will short out at some time which can cause any thing from the pc not booting to loss of just that port. If it starts causing reboots due to shorting even bumping the table could cause you to loose important data.
A picture of the broken port would help explain the situation better.
Here is the best image I could find for the purpose.
Behind the white rim is a metal housing which is where the port actually begins. If that housing is attached to the pc and not bent out of shape it should hold the usb devices well. The white tab shown with the 5 pins is what actually makes contact electrically. Which you said was intact. Since you say that is in place the only thing left would be the springs at the bottom of the image. They could have been bent out of shape or flattened. it might be possible to use a paper clip or a dental pick to slide under them and bring them back to tension. If they were flattened though it is likely they wont stay springy for long since they are so tiny you will be hard pressed to find a spongy/springy material to slide under them to keep the tension.