OK, let's get a few things straight here folks...
'calm' and 'farm' rhyme for most RP people, and many other English speakers. Neither actually has an 'r' in the pronunciation for these speakers.
For Scottish people, and other rhotic accents (ones which pronounce 'r' before consonants and pauses), 'farm' and 'calm' do not rhyme, and 'farm' does have an 'r' in the pronunciation.
Try here - type in 'farm' and 'calm' for Alan (Scottish) and then for Nick1, and you can hear the difference.
Many of you who are saying that 'calm' does have an 'r' in the pronunciation because it rhymes with 'farm', and if it didn't have an 'r' it would sound like 'cam' - I think you are confusing the spelling with the pronunciation. 'calm' and 'cam' for RP speakers both have three sounds, a 'k', a vowel and 'm', and the only difference is in the vowel (same vowel as 'father' for 'calm', and same as 'hat' for 'cam'). Hope we've cleared that up!