Hey Anders.
Short and sweet answers to your questions (others might chime in with more in depth explanations):
Scale lenght
In my experience, it really only affects how you approach the instrument physically.
Smaller players (such as myself) have reported feeling less encumbered when playing shortscale necks.
Some people will argue that the shorter scale has an effect on tonality and dynamics, on account of shorter strings vibrating at higher frequencies and though that is theoretically correct, this difference in my experience, has been mostly dismissable.
Strings popping out of saddles
Tends to happen to Jag/JM players that have aggressive picking styles. This problem is attributed to this saddle design, which are shallowly threaded, in order to allow players to customize their string spacing. This can easily be solutioned by deepening the grooves in the saddles to taste. More radical approaches involve swapping out the bridge for TOM, Mustang and "Intended for Jaguar/JM" designs. There is also an aftermarket part called a "buzz stop" which can be fitted to the tremolo unit, that increases the string tension over the bridge, which people have found useful in resolving pop-out issues.
Regarding the tremolo
This is really a question of taste but most of the complaints I've come across regarding that system can largely be attributed to two things:
1. faulty setup and 2. unreasonable expectations. When properly setup, Jaguar/JM tremolos, in my opinion, are probably the best compromise between tuning stability and functionality. Don't expect to be able to do Van Halen divebombs but this sytem will allow you to bend quite a bit more extensively than with a Bigsby or a Maestro... Some people like to fault the shallow break angle and long string length between the bridge and the tailpiece as the source of alot of buzzing and of unwanted sympathetic resonance. This is a matter of personal preference. The buzz stop will supress this to an extent but a great deal of people that play these guitars, do so specifically because of these properties. Alot of great music has been written because of this trem unit. You either like that about it or you don't.
You'll want to note that there is a Jaguar model which was designed to address these "issues". The guitar comes stock with a TOM style bridge and the trem has been placed closer to the bridge in order to increase the string's break angle. These are the Classic Player series. As a Classic Player player, I can tell you that though the issue of string pop-out has been fully addressed by this design, matters regarding sympathetic resonance are still very much in order.
Hope this helps.
Welcome to the team!
Last edited by laterallateral on Fri Sep 19, 2014 3:05 pm; edited 115,726 times in total