Is this a good example of the problem of unequal temperament (just to get it clear in my head what it was)

If you get a piano tuned in the old, unequal, temperament say C. Then the scale of C is correct, as are the sharps and flats (is this correct?). If you then tried to play in G or F then the F# in G and the Bb in F are not quite correct but you could get away with it. If however you tried to play in keys further from C the less the piano would be in tune and therefore unplayable in these keys. Is this a correct example of the problem?

The Well Tempered Clavier came out in the 1700's so I presumed this was the start of the move to equal temperament. However, fretted instruments predate this so did they evolve an equal temperament of their own or were they also unable to play in only a few keys?

Cheers