字が汚くて

[Muz1234]

字が汚くて

What does this sentence means? Does it mean, "The handwriting sentence is messy."?

 

[Joschl]

字が汚い:
Someone's handwriting is not neat/clear.
Someone has terrible/awful handwriting

 

[gengo]

字が汚くて

What does this sentence mean? Does it mean, "The handwriting sentence is messy"?

Right.

Also: the handwriting is sloppy / hard to read / almost illegible / chicken scratch / etc.

In the case of Japanese, it could also mean that the kanji are not written beautifully, even though they may not be difficult to read. So we might also say something like "His characters are childish."

 

[SoLaTiDoberman]

字が汚くて・・・＝The handwriting is terrible, so...

The latter half part is abbreviated, as is often the case with Japanese.

For example,
字が汚くて読めない＝The handwriting is terrible, so I can't read it.
(ラブレターをもらったが）字が汚くて、幻滅した＝The handwriting was so terrible that I was disappointed a lot.