Here’s what Garner’s Modern American Usage has to say about generally:
generally has three basic meanings: (1) “disregarding insignificant exceptions” <the quality of the acting is generally very high>; (2) “in many ways” <he was the most generally qualified applicant>; and (3) “usually” <he generally leaves the office at five o’clock>.
In contracts, the word generally appears in standard phrases such as generally accepted accounting principles. But more, uh, generally, it exhibits the problem that afflicts usually and substantially—all three words are vague in a way that goes beyond the vagueness of words such as promptly. (For more about usually, see the immediately preceding post, here.)
Consider the following, from a definition of “Event of Default”:
… the Borrower fails generally to pay its debts as they become due …
What level of failure would allow the lender to say that the borrower has generally failed to pay its debts? Who knows.
You could say instead fails to pay a debt when due, but that would cover inadvertent failure to pay a single insignificant bill, even if the borrower thereafter quickly pays the amount owed.
What level of failure to pay your bills constitutes default would always require that you take into account context, so I’m considering deleting generally and otherwise letting the chips fall where they may.