Spell checkers in word processors have reduced the number of spelling errors but don't solve all the problems. Some of the most common are listed below.
accurate (true), precise (reproducible)
advice (noun), advise (verb)
alternately (by turns), alternatively (in another way)
analysis (singular), analyses (plural)
assume (a hypothesis, theory), presume (a belief)
calendar (record of time, a register), calender (to press with a machine)
fewer (for discrete objects), less (for a collective term). Fewer stones, less sediment, less money, fewer pennies. (That Monty Python's decomposing composers are becoming less every year has meaning different from them becoming fewer every year.)
farther (distance), further (greater, more)
fiord not fjord. Note, the former is used in proper names in Canada
its (possessive), it's (contraction of it is)
loose (detached, slack), lose (misplace, be defeated) meter (an instrument), metre (the measure of length)
phenomenon (singular), phenomena (plural)
possess (to have or own), posses (plural of posse)
principal (main, chief), principle (rule, law)
quasi- (partly, seemingly), semi- (half)
stationary (not moving), stationery (writing paper) ('a' has a tail to keep it stationary)
thesis (singular), theses (plural); also hypothesis
verbal (in written or spoken words), oral (in spoken words)