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Notes on stability derivatives
(Originally by Ferram, being reformatted)
Regarding the various numbers that can be seen on the derivatives pane, generally, the absolute magnitudes matter less than how they compare to each other; the values can scale strangely as the plane grows and different parts get used.
Most values are color-coded based on their sign: red bad (opposite sign) and green good, as usual.
A parameter of the form Xy is shorthand for Imgur
##STATIC
Mw is the primary static stability parameter: it tells you whether the center of lift is in the correct position. If this is negative (red), the plane is going to rapidly depart in a backflip (or nosedive) at the slightest uncorrected disturbance. In mathematical terms, it's the first derivative of the pitching moment over normal velocity - i.e. angle of attack, effectively.
Yβ and Nβ are static yaw stability parameters. These will almost always be the correct sign at the same time, unless the dorsal fin has highly excessive area, and if correct basically make sure that the plane wants to fly straight rather than skate sideways.
Yβ is the first derivative of side force over sideslip angle, and Nβ is the derivative of yawing moment over sideslip. Nβ is exactly analogous to Mw, and must be always positive. Wings and the horizontal tailplane have a slightly positive effect on Nβ. However, the fuselage causes Nβ to decrease. Vertical tailplane, of course, strongly increase Nβ, even though it's possible to design aircraft without them (case in point: birds).
Lβ tells you if the plane is stable in roll due to sideslip. Roll angle itself doesn't directly cause a roll instability, but roll angle does cause some sideslip (plane's lift and gravity end up in slightly different directions, and this induces a sideslip velocity), and that sideslip can cause the plane to roll like mad. A lot of people who build planes with these afterthought-like vertical tails end up running into issues with this not being large enough compared to the other values.
Mq, Lp and Nr determine whether pure rotation in pitch, roll and yaw (respectively) will damp out. It really shouldn't be possible to get them into the wrong sign without something else being unstable, but I suppose it's possible for very strange configurations.
Zw and Xu are basically just the effects of lift and drag, respectively (Z is positive down) as you increase downwards vertical velocity (increasing angle of attack) the plane makes more lift. As you increase your forwards velocity, the plane makes more drag. If Zw is incorrect, you're plane is very badly designed. If Xu is incorrect, you have summoned the Kraken and should file a bug report.
The δe derivatives all tell you the effect of how the elevators and canards perform. If that's wrong, then somehow you've gotten your controls backwards; you want Mδe as large as possible while Xδe is as small as possible, since that means the most control authority possible with the least additional drag. Zδe is assumed to be correct for a standard tailplane design, so for canard designs it will be wrong (I'll make a change in FAR v0.13 to remove the coloring due to that reason).
Zq and Xq aren't really all that important, but they can make minor changes to the way a plane behaves under very large amounts of pitching.
Generally, Zu and Xw can be disregarded if their magnitudes are much less than the other ones. They basically consider how much additional velocity affects lift and how much additional angle of attack affects velocity, respectively; they can be the "wrong" sign at some angles of attack and Mach numbers due to Mach effects or nonlinear body drag.