Does this mole look dodgy to you

[Ladyoftheapple]

My husband noticed it on my back, he said he felt the skin was kind of soft and floppy

No it doesn't, looks like a skin tag but you could ask a pharmacist or if your surgery allow just send a picture to doctors. If you are concerned seek medical advise as the stress won't go away.

Looks similar to what I had once - a seborrhoeic keratosis. Although half of mine was a filiform verion and the other half looked like yours.

Always get it checked to be sure though.