|Something's not quite right here...|
Maybe the model of your dreams has a missing arm, head, backpack or half of its sword. This is probably the easiest fix of them all. If it's a model for an army you collect, I guarantee that in your spares box, you will have something suitable for this model. If not, there are plenty of places which can sell you parts, or even your friends might have something. The more daring of you might try to build your own parts (particularly if the model in question is a walker or tank), in which case, there are plenty of tutorials out there to help.
If the damage is on a tank and quite severe, you could consider covering it up with extra armour plates or replacement panels. Again, there are tutorials out there for making your own additional armour or details.
This problem can be a problem depending on the state of damage and the glue used. If it is super-glue, you can in theory snap the parts off, chip away the crusty build-up of glue and start afresh However if the super-glue is really....super...than a trick I've herd of is to briefly freeze the model, which will make the glue more brittle and easier to remove.
For plastic glue it is a bit harder, as poly-cements literally melt the two parts together. You may need to carefully amputate parts with your knife skills. If a part, for example a chest-plate, is blobbed in glue-stains, it might be best to replace the part, if the glue has attacked the details or blurred them badly.
Painting gone wrong
Dettol (brown) and Fairy Power Spray are two of the best ways of removing paint off both plastic and metal models. Simply throw your un-loved models into a glass jar, spray or pour (depending on your chosen substance) into the jar, so that the models are all immersed or covered. Give it a light shake, and leave it over-night, or at the very least a few hours. You should notice flecks of paint on the jar or discolouration that shows it's working. Take the models out. For Dettol submersions, you want to scrub the models in the Dettol fluids; scrubbing in water will create sticky gloopy blobs of paint, which are a pain to remove. You can rinse them after they have dried though. Washing Fairy-sprayed models in water is fine. It also smells nicer.
Once dry, the models should be in a far better condition. Note I have note mentioned resin models. I know from seeing a friend use it, that it can turn resin models into a rubber-like model, so I would research other methods. Fairy-spray might work, but again, check with others first.
So with that guide to renovation hidden beauty, I hope you consider buying the cheap-but-awful, in the hope to bring it back to life.