It's possible for a poor connection to prevent the battery charging properly but it would be hard to tell just by looking. You're right that bunging nails in isn't good practice. The connection needs a large surface area of clean metal, it doesn't have to be very tight. If you can't rotate the clamp on the battery terminal by hand it's probably tight enough.
It might be worth giving the terminals and clamps a clean with Scotchbright or the like and see if it makes a difference. If you decide the clamp is past it then
replacement is the best solution.
(Link to some clamps on Amazon)
Have you measured the current drain from the battery with everything turned off? That will tell you if there's a problem with the electrics, regardless of the state of the clamps.