I bought London Calling on ebay a while ago, and I noticed that the records are sort of…concave. I guess convex if you look at it from the other side. Anyway, I’ve noticed a bit of distortion from it, and the needle rides up and down quite a bit while it’s playing due to the irregular shape. Is there a way I can safely flatten the records out?
Never tried it myself, but there seem to be some useful suggestions here: http://www.boingboing.net/2006/05/17/cha_cha_and_mambo_tr.html
From my experience, you can’t flatten a warped record. The vinyl has stretched and is virtually impossible to shrink. I had a Sammy Hagar record that was left in the sun too long, I put it in the freezer then quickly recorded it to a cassette so I could listen to it. I later tried a bunch of weight (left on for a week) but that resulted in a permanantly distorted record.
People used to recommend putting the LP between two sheets of glass and then out in the sun for a while. That seemed to be the standard advice, but I’ve never tried it.
Late in the era of when LP’s were still the standard the record companies started using inferior vinyl and made the records as thin as possible. Cost cutting ruled the manufacturing process. It seemed like every record was full of pops and would eventually warp if it wasn’t already warped when new. There never seemed to be any way of correcting the problem. The turntable manufacturers were introducing tonearms that were designed to ride irregular surfaces. That seemed to be the solution.
I believe that the poor quality of the LP’s had a huge impact on quick adoption of CD’s by the public. The consumers were so frustrated they willingly adopted a new standard.
There are things you can buy to play warped records. A record collector I know has one, a vacuum type, which is mentioned here (scroll down the page). The linked page is for a stabilizer ring, but discusses the other kinds of things you can use. This article explains how to flatten a vinyl disc, but notes it’s not a fool-proof method. I always thought my friend’s vacuum turntable was really cool.
Sure, there was. Invent CDs. 
I have a huge collection of LPs from years gone by. The only thing I’ve ever found to be of any help are a spindle-spider and a quality turntable. The spindle-spider is a device that clamps onto the center spindle and presses down on the LP, flattening it a bit. I then play them on an ancient JVC turntable that seems like it will play a Frisbee if necessary…computerized tonearm controls and all that. Good luck with any other method.
Just get one of these:
The most endearing characteristic of audiophiles is that they don’t live in the real world.