What do I look for in used records?

One more thing: the 'bad' scratches can be nearly invisible in flourescent light. They are thin but deep, like a knife cut, usually the needle causes these. They almost always have a harsh 'tick' sound.
The 'non-scratch scratch' (called 'scuffing')are broad marks from brushing the LP against an object. These marks often make no noise at all. (if you cannot feel it with your finger or fingernail, it will probably play without a ticking noise)
Cleaning is all important. The dirty looking ones often are easier to clean, wash 'em and play! The clean looking ones sometimes have an overdose of dreadful grunge buried in the grooves, that is really hard to get out. they sound terrible until they are properly cleaned. They need to soak! to get that stuff out.

Wonderful, thorough introductory remarks, so far. My only extra thought is that certain scratches are less offensive sounding than others. If you find a famous performance or recording you really want to hear you can still take a chance that the basic audio and musical quality will make a $1 or less expenditure worth trying. Sometimes overlooking one or two "skips" lets one hear enough to still appreciate the magic left in the forty to fifty year old grooves. If there are multiple scratches try to pay only 25 cents. After trying a few, if the ticks and pops annoy too much then in the future go only for the visibly clear surfaces. Clear surfaces do not guarantee good sound, but it gives you a better chance.

Wdi...You can tell if a record is stereo or mono by the appearance of the grooves. Grab two records that you know are stereo and mono, and see what I mean.

Good general info from the folks above. LM-1903 is mono, as Pmotz indicated. LSC-1903 was the stereo version. "New Orthophonic" was RCA-speak for the superior equipment and techniques they developed just before the stereo era began in 1954. They used the phrase on both mono and stereo releases. As others have said, RCA records from this era were among the best ever made.

Do not assume that your mono pressing is necessarily inferior to stereo. Quite the contrary! Most 1955-65 RCA recording sessions were taped simultaneously on two seperate machines, one for each format. Since the mono machine used the entire tape for one track, it often captured inner details and dynamics better than the stereo setup. I have an RCA mono LP from that era, Arthur Rubinstein/Beethoven's 5th concerto. It lacks the width of stereo but it gloriously reveals the shadings of AR's playing and a million orchestral colors.

Entry level rigs and systems will not reveal everything that's on such a fine record, but that doesn't mean playing it won't be thoroughly enjoyable. Just take care your stylus is undamaged and your setup is accurate. If that record's clean it's a real treasure, and of course you already know how good the performance is. I have a current reissue on audiophile vinyl. Mine cost $27 but if your's is undamaged it may actually sound better. Good find!

Having bought several hundred used records in the past year, here are my observations.

I have looked closely at my used records which have persistent noise under a microscope and found that they have a slight roughness or tearing to the otherwise smooth groove walls that was presumably caused by damage from a bad needle. These are LP's that to the naked eye appear in excellent condition. The noise you will hear is a slight static or distortion at the more intense points of the music. Unfortunately, this type of damage is very hard to observe unaided but it seems to be quite prevalent. Visible scratches may or may not be a problem as many are just along the record surface and do not impact the needle as it plays deeper in the groove.
I agree with the posters above that stereo recordings are not better than their earlier mono versions. In general, I have found that the reissues from the early 80's on, even the ones claiming to be "audiophile" versions are inferior to earlier recordings. To me they just sound like the CD with the analog noise. They lack completely the "presence" that makes well recorded vinyl superior to digital. This unfortunately, confirms that vinyl is dead except for those who, like me, want to sour the earth for real old records. If you're planning on making up your collection from vinly recorded after 1984, I suggest you just go with high quality digital.