We present a pulse-timing analysis of Rossi X-ray Timing Explorer (RXTE) observations of the anomalous X-ray pulsar 1E 2259+586 from its 2002 outburst to 2010 October. We have the following objectives: to extend the work on the recovery stage after the 2002 glitch; to investigate the variations caused by the second glitch that occurred in 2007; to look for other unusual events, if any, that arise in the regular spin-down trend of the source. We find that the fractional change in the spin frequency derivative after the 2002 glitch is not stable as it decreased by an order of magnitude, from -2.2 x 10(-2) to -1.278(3) x 10-3, in about 2.5 yr. Using a pulse-timing analysis, we discover two small frequency shifts with fractional changes Delta v/v= 3.08(32) x 10(-8) and Delta v/v=-1.39(11) x 10(-8). While the first of these shifts is not found to have a fractional frequency derivative change, the second has . We interpret these frequency changes as positive and negative microglitches, similar to those seen in radio pulsars.