Your question appears to be based on some incorrect premises. Many things can be repaired without looking like a stitched or glued together patchwork of parts. Transporter/replicator technology alone would allow his skin to be repaired fairly easily without leaving visible scars.
Secondly, Dr. Soong took great pains to make Data human-like down to the smallest details. This is why he's able to eat and drink normal food, breathes, blinks (based on a Fourier series), is anatomically correct, has an aging program, has hair that grows (at will), and is even able to dream. It's therefore likely that Data's skin also self-repairs to some degree like a human's, and there's no evidence that it doesn't.
There are no canonical sources describing Data's skin, but a close-up of his hand shows that his skin (Data refers to it as molecular fabric; in a later episode, it's described as bioplast sheeting) has a cell-like structure:
Lastly, there's no rule that says only carbon-based materials can be self-repairing. Here's a clear counter-example.
I would assume that Data's skin is probably resilient enough to resist fatigue at his joints, or the bioplast sheeting has some basic self-repair functions to counter deformation stresses. When his skin does need manual repair, it would be a simple matter of grafting new bioplast sheeting over the damaged area. If a dermal regenerator can heal wounds without leaving scars, then how Data's skin can be repaired without scarring should require no further explanation.