These are all Elementary School- or Junior High-level errors, and you should never make them. Never.

• Their/they're/there
  • Their means "it belongs to them"
  • They're is a contraction of "they are"
  • There is a location, distant from here.
• Effect/affect. This is a hard one to get right, but not impossible
  • Affect can mean "emotion" or "attitude"
  • Effect can mean "to make happen," as in "effect change"
  • Effect can mean "results," as in "the effect of the new procedure was..."
  • Affect can mean "influence" you, as in "how did that affect you?" This is easy to confuse with the meaning of "effect" above, but remember the other meaning of "effect" and you should be safe.
• Who/whom. Turn the sentence into a question: instead of writing "he is the one whom does the job," ask "who is the one who does the job?" It's easy to answer correctly "he does the job." If you say "he", use "who", if you say "him", use "whom."
• "I feel badly." Unless you're a psychopath, you're probably fine at the act of feeling -- but what the previous sentence really means is "I am bad at feeling." The correct phrasing is "I feel bad."
• Premier/premiere -- it shouldn't be easy to get confused between the two meanings here:
  • Premier means "best" or "leading", as in "Cal Ripken was baseball's premier shortstop during the 1980s."
  • Premiere means "to show for the first time" as in "the play's premiere was on Friday."
  • Occasionally, Premier (always with a capital P) will refer to the head of government of a country. This is not a common use.
• Wary/weary
  • Wary means "watchful and mistrusting," as in "I'm wary of our new boss."
  • Weary means "tired." People often misspell "wary" as "weary," which, as you can imagine, changes the meaning of the sentence entirely.
• Capital/capitol
  • The capitol is where the government sits
  • Capital is
    • Money
    • A "capital idea" is a good idea
    • The top of a column