Probably your biggest concern would be if you somehow shorted a transistor. If your DMM has a diode check feature, use this. Otherwise, something in the 2000 Ohms range may do it.
On your schematic, the transistor will be a circle with three leads going in. Usually, the lead that is perpendicular to the straight bar or line is the base. The lead with an arrow on it is the emitter. That leaves the collector as the last lead. Hopefully, you will have high resistance between emitter and collector. The other checks are as Grainger has described. Besides differences in meters, the associated circuitry can make this test dicey sometimes, but if you see anything approaching zero or very low Ohms, it is probably worth pulling the transistor.
Usually small signal transistors of that sort can sit on the PC board without much trouble, provided they're not being run in such a way as to be dissipating a lot of heat. While it is generally better to mount them in such a way as to be able to see some light between them and the board, you may well be OK.
As you say, a designer will be able to tell you for sure.
