1. Kate is listening to music with headsets on a smart phone.

2. Kate is listening to music with headphones connected to a smart phone.

3. Kate is listening to music wearing headphone attached to a smart phone.

(Are the sentences grammatical? Would you correct errors? Thank you.)

1 would be correct if you use the singular form: "headset."

2 is correct.

3 would be correct if you use the plural form: "headphones."

(A headset is made up of headphones ... but not vice versa!)

=)

Also in #1, the word "a" needs to occur before "headset."

All three sentences are grammatically correct, but there are slight differences in their structures and phrasing. I would make a few corrections to improve clarity:

1. Kate is listening to music using headphones on a smartphone.
2. Kate is listening to music with headphones connected to a smartphone.
3. Kate is listening to music while wearing headphones attached to a smartphone.

These revised sentences are more precise in describing how Kate is listening to music with headphones connected to a smartphone.