Even if you've never tried to set the intonation on a 6-string guitar with three saddles, you've probably noticed that chords tend to sound out of tune as you move up the neck of a stock MM/DS. And especially for guitars with 22.5" scale necks, you've probably noticed that it can be a problem keeping the guitar in tune, period. There are ways around the inherent shortcomings (no pun intended) of shorter scale guitars, though:
Short-scale guitars are more difficult to keep in tune because the shorter scale means less tension is required to tune a string to a specific note. The same thing is true if you tune the strings on a guitar down a half step like Stevie and Randy did, or even lower like Tony Iommi and countless other metal guitarists. Unless you use a heavier gauge, the strings will feel too "floppy" and you'll lose output (lower string tension also means less string vibration, which means less output from the pickups). I used a set of light gauge strings on my 22.5" scale '50s Musicmaster before I switched to a heavier gauge. It was nice being able to bend strings like I was Buddy Guy, but ultimately heavier-gauge strings helped it stay in tune and made chords sound better.
The gauge of strings you use is up to you, depending on the style of music you play and whether you tune down. Originally (ca. 1966), both 22.5" and 24" scale MM/DS/Mustangs were factory-equipped with heavy gauge strings (low to high, .052 .044 .034 .026 .016 .012). From a practical standpoint, I recommend heavier-gauge strings if you don't play much lead guitar, because the higher string tension in the wound strings makes for a better rhythm tone. For standard tuning, I prefer GHS TNT strings ("thin-thick" -- low to high, .052 .044 .030 .017 .013 .010) on my 22.5" scale red Musicmaster. On my 24" scale '65 Musicmaster II, I have GHS GBM strings ("medium" -- .050 .036 .026 .018 .015 .010). I should probably mix and match strings to even out the tension, but I haven't tried that yet. You can also use "rollerwound" strings (wound strings that are slightly flattened, which will increase the apparent string tension). In addition, I've asked Fender 3/4-scale guitar authority Tim Pershing what strings he prefers. His reply:.010 to .046 (light gauge) on the 24" scale guitars usually work and feel just fine to me. I have that gauge on a few of the 3/4 scale guitars, but most have a set that GHS makes called "light plus": .0105 to .048. It adds just the right amount of "tension" without making the action feel too stiff. I have used "medium" gauge (.011 to .050) and "light top, heavy bottom" things (.010 to .052) but I never really liked the feel of those strings.I guess the best advice here is, use what feels best to your hands. See what's available at your local music store, and go from there.
Finally, the lone string tree on the headstock of every MM/DS should NEVER be screwed down all the way to the headstock face! You need some downward angle on the B and high E strings, but screwing it all the way down can cause the string to bind at the nut. Use a spacer or just don't screw it in all the way. Start with a height of about 1/8", and go from there. Allparts stock #AP 720 includes two trees and two ~3 mm high plastic spacers, for $4. More recently, StewMac now includes two metal spacers (one 2.5 mm high, the other 5 mm tall) with their "butterfly" string trees.