Copper and lead are actually magnetic -- more accurately, they're diamagnetic. Thus, in theory, a magnetic field in front of the copper-jacketed lead bullet could resist the bullet's motion and, along with a field around it, suspend it in the air.
In reality, the strength of a magnetic field capable of stopping a supersonic bullet1 at point-blank range is astronomically staggering, and would have all kinds of effects on ferromagnetic materials all around (except that Magneto is quite clearly able to shape and limit his projected magnetic fields such that they only affect what he wants them to, as pointed out by a few commenters below); someone better at the math than I could probably tell you how much energy would be required to bring a typical FMJ bullet to rest from a velocity of at least 360m/s in the space of no more than half a meter. Even one strong enough to suspend a bullet in mid-air is mind-boggling. (Diamagnetic forces are generally very weak, and both lead and copper have very high resistances.)
Further, once stopped, the bullet simply has no more momentum, period -- completely negating Magneto's implied threat by leaving it suspended in the poor cop's forehead (as well as showing that the slow forward motion of the bullet during his little chat with Xavier's proxies was his deliberate doing, not an effect of him holding the bullet back).
Basically, the whole scene is lazy writing (bullet = metal = magnetic!) done solely for the Rule of Cool (WARNING: TV Tropes link!). Even granting the existence of the controlled manipulation of magnetic fields (such as Magneto's powers), this scene is just not possible, and you're exactly right -- Magneto should have effectively no more control of lead-and-copper bullets than he does of the plastic darts encountered later. (But see next section below.)
On the other hand, it is conceivable (albeit unlikely) that the cops here were loaded up with armor-piercing rounds. These are generally steel- or brass-core bullets (the
heavier, harder metals resisting deformation on impact, thus resisting the dispersion of their inertia), the former of which is more conceivable to be affected by Magneto's powers (I'm unsure about brass, however). On the third appendage, bringing a heavy steel bullet from supersonic velocity to a complete stop that quickly would, still, require a magnetic field of such staggering power it defies belief even in a world where shape-shifters and metal-clawed mutants are commonplace.
All of that being said, though, as pointed out by several commenters below Magneto's powers seem to be less reliant upon magnetic forces, and behave more like telekinesis that is (usually) limited to metal objects (perhaps because he believes his powers are magnetic, and thus he subconsciously limits himself to only those materials he believes can be affected by such). If that's the case, then stopping a bullet is merely an act of will, and magnetic forces per se don't really play any part in it. To be sure, he does seem to have at least some form of limited telepathic powers, in that even without his telepathy-blocking helmet he does seem to be able to resist Prof. X's telepathy to some degree; in a world where telepathy and telekinesis seem to be linked (if not outright confused), that could be a sign of a telekinetic basis to his magnetic personality (nyuk nyuk!).
1While I'm no firearms expert, it looks to me like a 9mm handgun firing a standard FMJ round, which makes sense as the venerable 9mm is the caliber of choice among most police departments in this country; from what I've found that generally has a lower-end muzzle velocity of 360m/s, which is of course greater than the speed of sound of ~340m/s and, thus, is supersonic.