You're assuming each week WAS a week. They didn't do that in classic TV days. Time between episodes was irrelevant because nitpickers weren't as rampant, and nobody cared.
It took place 1950 or 51 - 1953. And the time evolution WAS explained from time to time.
--Ted
But didn't they have a Christmas episode, like, every season? That would imply a year passes between each season.

Or at least a reference to Christmas? Or the Christmas episodes not "evenly spaced" to suggest a logical progression of time?
It's been a long time since I've been able to watch the series so I'm fuzzy on the details. But I think the Christmas episodes/references in MASH suggest that each season WAS supposed to represent a passage of one year.
There were four Xmas eps, and only one occurred on the Day itself.
Here's an amateur timeline I trot out when these threads come up :
September-October 1950 - Henry breaks ground; Trains Radar
November - Departure of Ugly John, SpearChucker and the reffed-but-unseen TV version of Duke Forrest
. Hawkeye appointed Chief Surgeon.
December - 1st Christmas
January 1951-November - Forms the bulk of Klinger's escape attempts, phony tries at types of discharge. Bulk of Burns/Houlihan reports and attempts at ousting Henry. 90% of the first 3 seasons eps take place in 1951.
December 1951 - Henry receives his discharge notice, to take effect the next month. 2nd Christmas. Trapper's notice is issued, but is lost in army mail til the next month. Potter and BJ are informed of their assignments.
New Year's, 1952 - Henry makes a toast to the New Year that Potter repeats a year later.
Early January , 1952 - Formal discharge and subsequent death of Lt. Col. Henry Blake. Hawkeye manages to get a pass to Tokyo (From Burns?). While he's gone, Trapper's delayed orders surface, and he is gone by the time Pierce gets back. Enter BJ.
Late January - Frank is relieved of command by Colonel Potter, who it should be noted, gets no reports written about him.
Over the course of
1952, Klinger begins to cross-dress less often, relying on scams for his ticket out.
June - Margaret becomes engaged, ending her affair with Frank.
July 4th - 'You Creamed IT, you NINNY!'
Late July - Hawkeye is reunited with Carlye.
Mid-Late August - Margaret marries Donald Pinobscott. Frank is given leave time, has mental breakdown. Is promoted and sent home.
Early September - Arrival of Charles. Hawkeye and Radar have falling out over his wounding; reconcile. An extended newsreel of the year's earlier Olympics causes one to be held at the 4077th. Charles makes extensive bets on baseball, not truly understanding that the season is mostly decided by that point.
November - The events of 'Comrades In Arms'. By month's end, Margaret has decided to divorce Pinobscott. BJ grows a moustache.
Early December - Margaret's short marriage ends in a final divorce. Depressed before Christmas, Hawkeye invades the peace talks. Charles' sister suffers heartbreak when her engagement is undone by ethnic bigotries.
Late December - Mulcahy has a crisis of faith on Christmas Eve; Charles is seen as Scrooge but in reality, his efforts to play Secret Santa for Korean orphans clashes with the reality of war; Radar's gift of a tobbogan cap sent by Winchester's mother raises his spirits. On Christmas Day itself, Pierce, Hunnicutt, Houlihan and Mulcahy try and fail to save a dying soldier so that his family will not associate Xmas with his loss. They end 'pushing' the time of death to 12/26. That next morning, Klinger's efforts to bring the UK's Boxing Day to the 4077th leads to another pointless appearance of the 'everyman' Cook. On New Year's, Potter quotes Henry from last year. The camp then reviews footage of the Baseball League Pennant races, renewing Winchester's anger towards Klinger.
Early January, 1953 - Death of Edna O'Reilly's brother Edward; Radar is discharged.
Mid-January - (speculation) Finding out that Zale helped the other unit in 'Goodbye,Radar' steal their backup generator, Potter kicks him out. His sort-of replacement, Luther Rizzo, is a questionable improvement.
May - A would-be beach outing never reaches the beach. When Hawkeye sees a mother smother her newborn infant to keep it from alerting enemy patrols, the pressure of the war finally cracks Pierce, who spends time away from the 4077th recovering.
July - End of hostilities; Dissolution of 4077th MASH.
Early August - Most former members of the unit arrive home.