If a paladin takes a mount with permanent spell effects (best two I can think of is a blink dog and a displacer beast), would the rider share the benfits of blink/displacement?
I don't believe the Paladin receives the powers of his mount, because I don't remember the Paladin receiving the power to control other mounts if his mount is high enough level.
The question, though, is not does the paladin share the "blinking" of a Blink Dog, for nothing in the rules even suggests the paladin "shares" spell-like abilities (or even spells_ from his mount.
The question, then, is, "Would ANY rider "blink" with a Blink Dog?" I suppose so; the rider would be considered somewhat like equipment, I think.
Well, nothing suggest the paladin share the ability of his mount. But if he doesn't blink with his mount, he'll fall through it! I would say that the blink dog shouldn't use his blinking ability while you are riding it.
Neither the Blink dog or the displacer beast (A Lawful evil beast BTW) are on the optional mount list in DoF probably because of situations like this.