I would doubt it. Probably the best example of both of the terms is "misfeasance" and "malfeasance". Both attach to the Anglo-French root word "feas-" which is also the root of the modern French "fais" (to do/to make), and usually refer to poor performance in public office (the terms can apply to any job performance though).
However, the terms are distinct at law: "misfeasance" is an unintentional failure to satisfactorily perform the duties of the job, due to incompetence or abdication. "Malfeasance" is an intentional abuse of the powers of the job to cause damage to the office or its constituents.
I cannot think of another use of these two prefixes side by side, but use this rule of thumb: If you want to mean "bad" as in evil, use mal-. If you want to connote "poor" as in "at a low level", use mis-. The loss of a baby in utero due to force majeure or a "poor" uterine environment is a "miscarriage"; it's not a "malcarriage", as the woman did not intentionally use her womb to abuse her unborn child. By contrast, a "malodorous" person or thing literally "smells evil", and figuratively speaking may have a "stink" around their actions or personality. The word is not "misodorous", as most "malodorous" things consciously chose or were specifically designed to smell bad; it's no accident.
The Oxford English Dictionary writes that there are forms in which beware is inflected. For example, they write that the secondary sense is:
As an inflected verb.
1598 J. Florio Worlde of Wordes, Raueduto, bewared, espied.
1606 N. Baxter Sir Philip Sydneys Ouránia sig. Kiij, Bewaring of too hot combustion.
1669 Milton Accedence 18, I had bewar'd if I had foreseen.
1672 I. Newton Let. 29 Jan. in Corr. (1959) I. 84, I stirred them a little together,
bewaring‥that I drew not in breath neare the pernicious fumes.
1700 Dryden Chaucer's Cock & Fox in Fables 253 Once warn'd is well bewar'd.
1860 R. W. Emerson Fate in Conduct of Life 41 We beware to ask only for high things.
1870 Echo 17 Oct., Showing the greatest respect‥and bewaring of the slightest insubordination.
However, the primary sense of the verb is without these inflections. In the associated OALD, they only include the non-inflected type, and say that beware is only used in infinitives. It is this sense that most people use--without adding tense endings.
The author seems to be using only this sense of the verb, and referring to it as the sense of beware. He is not wrong in that this is the sense that most people will recognize. However, this does not mean that there have never been inflections added--they just didn't catch on into popular use. Now, the secondary use listed by the OED is not likely to be found anywhere except in old quotations. Beware is "defective" because it is a verb which doesn't take inflected endings (at least, not any more), so it has turned itself into a fairly irregular verb.
Best Answer
Henry is of course technically correct: You can't just slap re- onto any verb. But I believe the spirit of your question is: Are there verbs that are correct to put re- in front of, even though the result is not in the dictionary? And further, are these plentiful enough that your friend was merely being sloppy in their phrasing, rather than wrong in spirit?
My answer: Definitely yes, and yes.
My dead-tree American Heritage Dictionary even has this note following its entry for re- (note the first sentence):