Anyone else have issues with their CD player/transport not playing slightly damaged CD's?

Putting this out to the general audience for comments/impressions.  I had an Oppo BDP-103 CD/DVD player that would play nearly any CD you stuck in it, scratched or scuffed; if it started skipping or choking, usually the CD had a lot of scuffing or a large scratch on it, to which I understood and would go on to another disc.  I acquired a Cambridge Audio CXC CD transport, and it is much more picky about the quality; if the disc has the least amount of soft scratches or inner-diameter scuffs, it behaves badly.  I was wondering if everyone has these issues, is this a problem that affects lesser or better transports equally, what kind of transport you have?  
If your CDP is not new then perhaps it needs lens cleaning (lens cleaning CD).  Inner diameter scuffs are worse being closer.  If nothing works, then you can rip CD and record CD-R.
Unfortunately I have found there to be a considerable difference between the tracking ability of various CD players.

One of the very best in my experience was a Technics SL-PG480A from the late 90s.

We used to have this horribly scratched (all over the face) best of Motown 2CD box at this studio where I did some voluntary work and it always made me smile when the Technics CD player was able to sail right through.

I wasn't smiling as much when my much vaunted UK tuned midrange Sony deck couldn't do the same. Yet the Samsung drive on my Dell PC could still rip it.

In my experience car CD players and those on midi systems are usually worse.

I have read that one of the earliest audiophile CD players from Cambridge actually featured a readout that would illustrate the amount of error correction in real time.

It's a pity that more manufacturers didn't include that feature. Maybe their health and safety departments figured all that constant uncertainty wouldn't be good for our sanity!

Anyway, in your case it could be worth taking off the lid and giving the laser a very gentle clean with a soft bristled artist paint brush - NO COTTON BUDS.

If you want to use some isopropyl alcohol then you should finish with a wipe of the same brush damped with some distilled/ purified (boiled) water afterwards.

If it's a case of fading laser power then have a look online to see if you can boost it for now via one of its neighbouring pots.

I'm sure Cambridge would be happy to advise. Don't be shy, most manufacturers in my experience have been great in sharing out advice.
Agree with kijanki. Try cleaning the lens. There certainly are differenced in transport tracking sensitivity though.
I had a NAD 538 that when new had a hard time with disks especially CDR's. Traded up to a 546BEE that would play anything.
My Pro-Ject transport hasn't encountered any problems yet. I will test.
Thanks for all of the suggestions and your experiences.  It is a few years old, one of the first version and not the second. I have a CD cleaner coming but if I get some spare time I will open it up, and use a soft brush to clean the lens.  If I start having a lot of issues I'll be looking for something else.  I had a 6-CD carousel changer in my old BMW 328i (worst car stereo I ever had, incredibly) which scuffed a lot of my favorite CD's and made them unplayable in nearly everything BUT the BMW player.
bikerbw, I have two cleaning CDs: one with tiny rubber brushes and another with holes that create air turbulence.  The first one works better, but the second is gentler, being contactless.  Few people reported success with tiny amount of mineral (sewing machine) oil on laser guide rails. 

I had once Cambridge CDP with Philips mechanism.  It had magnetic clamp holding CD down. Felt on this clamp wore out leaving gap and CDs wobbled a little.  Since you will open it to clean with isopropyl alcohol you can inspect things like that as well. 

I have cxc. Its not about your lens or anything. Its just because purely the player. I have a problem same as you since day 1

My Oppo 103 has never had a problem playing a disc. Even played a disc that was so horribly scratched it wasn't shiny any more. Convinced myself a brand new disc would sound better. It didn't. it sounded identical.