Dropping the low E to D reduces some of the bending forces that string applies to the neck. The neck moves slightly because of that reduction, and tension on the other strings changes slightly. If you use a meter for tuning, you may actually be able to see a few cents difference. Typically the A will be tighter, and perhaps the treble E looser. Generally this effect is more noticable with thinner, more flexible necks. The only guitar I've ever seen that seemed immune to this shift was one of those aluminum-necked Ovations.

Dropping into DADGAD from EADGBE eases the whole neck backwards significantly, and can even make a noticeable difference in the action on some guitars. That can affect intonation, because fret spacings and bridge positioning compensate for the effects of string heights and sizes. The top and neck may also take anywhere from a half hour to a couple of days to settle completely when after a large change in tuning. Using different guitars for different tunings can really simplify the problems often encountered.

One thing you might try is always tuning each string *up* to the right pitch. If you overshoot and tune sharp, then drop at least a 1/4 step low and try again. This keeps all of the friction and slack in the system working in your favor with the increasing tension caused by bending strings.

(And the comments above about string gauging and aging are right on target. Strings "work harden" with playing, which makes them drift sharper because of the increased section modulus. The gaps between the windings get filled in with debris from fingering, which also makes the string less flexible. I tend to change them whenever the 4th harmonic starts getting dull.)

~S~