My opinion for an "ugly Abe" is simply one beyond being desirable.
This can be from being worn out, burnt, or worse. Below is the Treasury technical terms, for me either can be "ugly."
The Treasury Department has prescribed regulations regarding uncurrent and mutilated coins.
Uncurrent coins are whole, but are worn or reduced in weight by natural abrasion. They are easily recognizable as to genuineness and denomination, and they are such that coin sorting and counting machines will accept them. Merchants and commercial banks will generally accept or refuse these coins at their discretion.
Mutilated coins, on the other hand, are coins that are bent, broken, not whole, or fused or melted together.