Fewest Runs scored in a month, since 2000 (24+ games):
45 April 2004 (Expos)
64 September 2002 (Tigers) 66 (Projected) June 2011 Angels
72 April 2011 (Padres)
74 September 2003 (Mets)
75 July 2010 (Mariners)
76 July 2001 (Mets); June 2003 (Dodgers)
78 September 2010 (Dodgers, Mariners)
79 August 2010 (Mets)
The dismal month the Angels are having offensively is odd not only because they've usually been solid over the last 10 years (especially in 2009, when they ranked 2nd in runs). They were scoring runs just a month ago, ranking 11th in runs scored in May. In May, they hit a respectable 22 HR, but they've only hit 3 through 16 games in June. That means that 24 players have outhomered them so far this month.
A lot of players have struggled, and Torii Hunter was probably having the worst month of all (.137, 0 HR, 3 RBI in June). He did go 3-4 tonight with an RBI in their 4-3 victory over the Mets, which is a good sign. They've been scoring more runs of late too(15 R in their last 4 games after 15 in their first 8 games of June).
Update (6/21): They've now scored 47 runs through 17 games, and they have 8 more games in June. After a (relatively) huge offensive game on Sunday (7 R), they're now on pace to score 69 runs. They're final 8 games are against the Marlins (2), Dodgers (3) and Nationals (3).
The Marlins are reeling. The usually strong Dodger pitching is off this season, and they're ranked 22nd in ERA (and 19th at home). The Nationals are 10th in ERA, and 3rd best in June. They've hit better of late, but it's going to take a big offensive surge to avoid having on the worst months in recent memory.