When D'Artagnan meets Aramis, Aramis is with a girl. When D'Artagnan kisses the girl, the background is an obvious backdrop for it does not match the background in the long shot. The types of trees are different and the river is missing.
The opening narration mentions the year 1648, implying that Cardinal Richelieu died then, and the loss of his "strong hand holding the country together" was the beginning a period of great instability in France that led to the events depicted in this film. However, he passed away in 1642, leaving 1648 to be interpreted as the year this story takes place. The problem with that is the fact that Queen Anne, whose own death is indicated here, died in 1666 when son Louis XIV was 27 years old and long since reigning on his own, not the prepubescent boy for whom she acted as regent seen here. Said regency ended in 1651, not 1648.
As Cornel Wilde chops wood in his first scene, there is a "THWACK" sound effect for each chop. Then, when he throws down the ax onto the grassy ground, the "THWACK" effect is used again. However, there is another fallen tree just beyond the one he is chopping on, and the ax could very easily have landed on it, creating a similar blade/wood impact for which the same sound effect would be appropriate.
As with all movies made at the time of this one, the weapons used were epees, not the historically correct rapiers. This is particularly notable given the cutting for presentation on television.
The three male children of the legendary Musketeers mistake Clair Athos for a "pretty boy" despite the character being played by the beautiful Maureen O'Hara who looks nothing at all like a boy.