Check the size of the microscope.  Many of the introductory and elementary student models are 3/4 size or smaller.  This is ok for younger students but children over 13 years old and adults might prefer a full size instrument.  Generally these smaller microscopes are from 11 to 12 inches tall and the full size microscopes are 14 inches tall and up.

If you do choose a 3/4 size microscope we recommend you select one with a stationary stage and a moving tube (to focus).  The instruments with the moving stage and fixed tube seem to have a universal problem with stage drift.   In the full sized varieties, this is not a problem so the moving stage is not an issue with them.  See more on stage drift below.

Materials and workmanship:  Basic frame and components should be metal, although some small parts may be of plastic.   Evaluate the general appearance of all optical and metal surfaces.
  

Check the focusing mechanism:  The rack and pinion type is the most reliable and should move smoothly when the focus knobs are turned.  There should be no rough spots.  We do not recommend microscopes with a single "intermediate" focusing knob.  If your microscope goes to 400 or 1000X, it should have both coarse and fine adjustments.

Check dovetail in the focusing track (rack and pinion):  Look at the type of metals used to assure that improper materials will not cause problems later.   Check for excessive grease on moving parts.

When focusing, some microscopes have a moving stage, others have a moving eyepiece tube.  If the stage moves when you focus, check stage drift by pushing down slightly on the stage with fingers.  It should not move.   If the stage is stationary and the eyepiece tube moves, likewise check drift by slightly pushing down on the eyepiece.  On some 3/4 size microscopes with a moving stage,  just moving the slide around on the stage will push the image out of focus!  This is extremely frustrating when you are trying to move a slide around at high powers.

Look at the alignment of the stage and nosepiece:  For example, if the stage is tilted just a tiny bit, your specimen will continually be out of focus on one side or the other.

Check for "backlash" by focusing all the way to the top and bottom and try to turn the knob further, looking for slight motion.  This tells you how well the rack and pinion gears are matched.

Check the slip clutch by continuing to turn the focus knob even after reaching some resistance.

Check parfocallity:  With a slide on the stage, the image should remain relatively close to focus when changing objective lenses.  Only a slight adjustment should be required to sharpen the image as objectives are changed.

Check parcentricity:  Start with the lowest power objective and center your specimen.  Move up to successive objective lenses and the area should remain relatively centered. 

Check for cleanliness:  With no slide on the stage, dial in your highest power objective lens, adjust the diaphragm to the smallest opening, turn on the illuminator and look through the eyepiece lens.  If you see dust particles, turn the eyepiece lens.  If the dust moves, it is on the eyepiece.  If it doesn't move, it is likely on the internal prisms.

The quality of the objective lenses is one of the most important characteristics of a fine microscope.  The better the lenses (and usually, the more expensive the microscope!), the sharper the image.  In a side by side comparison, you might be able to notice a difference!