What date range is being referred to when someone says {date} is in the first week of {month}?
Conversely, what about: {date} is in the last week of {month}?
Is the first week of April the first week that is entirely in April or is it the first week that contains the first of April? Of course this all changes when considering whether the start of the week is Sunday or Monday.
There may not even be an "answer". In that case I'm interested in the most common usage.
Edit:
This SO post and this mailing list are what have caused me to call the meaning into question in the first place.
In my (AmE) experience, the phrase is ambiguous and can mean any of the first week containing a date in April, the first week in which more days are in April than aren't, or the first week entirely contained in April, with the middle option being the most prevalent.
For example, if April 1 was a Friday or Saturday, in most circumstances, I would not expect the week of Mar 25/26-Apr 1/2 to be described as the first week in April.
Due to this ambiguity, this phrase is normally only used when giving rough estimates of dates where precision isn't necessary. If you want to precisely specify the range, use the actual dates.
People use it both ways. The most common way I hear it depends on the length of the first Monday-through-Friday week. If there are four or five weekdays in the first week, then it usually means the first week (Sun-Sat) containing any part of April. Otherwise, it means the first 7 days of April.
Sometimes people use it to make a date sound sooner, in which case it will mean the first 7 days of the month. For example, I may say your auto repairs will be complete in the first week of April. If April 1 is on Sunday, then you can pick up your car on Monday April 9th (since we're closed on the weekend).
Overall, I would say it varies dependent on regional, local, and family usage, and that both meanings are commonly considered correct.