Maverick has a nice post here about dubious philosophy of mathematics. Numbers are not physical objects, therefore they are in the mind, goes the argument. Valid or not? Read his post.
Anyone who has taught first year undergraduate students has a box of arguments ready for the common arguments that all beginners in philosophy seem to make. For example, the confusion between epistemological questions (how can we ever know the truth?) and semantic ones (what exactly is truth).
My favourite is the one I mentioned in the comments section somewhat earlier. It is argued that fictional names (or names for numbers or abstract objects), since they cannot name anything real, must name ideas in our mind. Thus, 'Pegasus' is a name for my idea of Pegasus. For this, we reach in our box and reply "But the phrase 'my idea of Pegasus' names my idea of Pegasus, surely?". They think for a bit and then see the point. The reply is mentioned in Quine's *Methods of Logic*, but is much older than that.
Brandon (at Siris) had a nice post a year or so back about the difficulties philosophers encounter in arguing with non-philosophers. I can't find it, however.