Recently I posted the following question to the alt.fan.cecil-adams news group on the Internet:
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BPH replied: “You’re incorrect. The former is not proper, and the latter, while not improper, is verbose, even though it is common. ‘Whether’ denotes a differentiation between several choices, and should not be used with a single antecedent. The proper word to use for the subjunctive clause in the first sentence is ‘if,’ as in, ‘I don’t know if it will rain on Monday.’”
To which FH replied: “On what planet-of-the-hyperactive-alien-schoolmarms, Bub? Thus spake the American Heritage Third: ‘whether 1. Used in indirect questions to introduce one alternative: We should find out whether the museum is open.’ A usage note under the definition of ‘if’ specifically discourages the use of ‘if’ in such cases because it often creates ambiguities.”
As you rightly surmise, there are instances in which it is wrong to append “or not” to “whether.” The test for determining such instances is whether or not you can delete “or not” without affecting the sense of the sentence. For example, in the preceding sentence “or not” adds nothing to the sense and is thus superfluous, if hard to resist. Not so in your sentence #2. Regarding sentence #1, both Frank and the AH3 are correct in pointing out that though “if” and “whether” are more or less synonymous, “if” can be ambiguous in some circumstances. The AH3 example is “Let her know if she is invited,” which can be interpreted to mean “Let her know whether she is invited” or “Let her know in the event that she is invited.”
