If it is just a dirty record with stuff in the grooves, you might try a product like GruvGlide. I've never tried this but some people have claimed good results with it.
http://amzn.to/UvYuR5If the record just has bad scratches that won't let the needle (or stylus) stay in the groove, then cleaning probably isn't going to help. You can try cranking up the tracking weight to the highest amount allowed by your needle (maybe 3 grams?). With any higher amount, you risk spoiling your needle. If this gets you through the spots that skip, record your LP into an audio editing program and make yourself a disc or mp3 so you never have to play the vinyl again.
I know you've been into vinyl for a long time but now, if you're not already doing so, you might like to take the next step of fixing up your recorded albums in a digital sound editor so they sound the best they can. I've been doing this for nearly 20 years and it can make your collection sound great and it's kind of a fun challenge to see how close you can restore a song to it's original studio quality (or sometimes better).
If you have a skip on one place but in another place the same few seconds of music is fine, you can copy the good part and replace the bad part and it can be impossible to hear that there was any problem to begin with.
Good luck on it.