Believe it or not... grinding into reverse is a very very very very common thing... and is not really a bad deal... There is no synchronizer for the reverse gear so there is nothing in the transmission to get the shafts at corresponding speeds...
first i'll explain the shafts of a transmission... the input shaft connects directly to the clutch, or the flywheel when engaged... the input shaft is always directly geared to the layshaft.... the layshaft spins gears which are always engaged to gears which spin FREELY AROUND the output shaft... and there are "dogs" (gears with teeth on the sides) connected to the output shaft which slide back and forth and connect to teeth on the sides of the various, constantly spinning gearsets, to finally connect all three shafts
as the transmission sits in neutral, clutch petal out.. the input and layshaft of the transmission are always spinning, but are not connected to the output shaft by any selected gear.. when you press the clutch, the two shafts remain in motion because of their momentum... and even possibly from a minor viscous wind friction in the clutch from the flywheel... when you move into a forward gear, synchronizers on the dogs allow you to match the layshaft to the output shaft to their corresponding speeds...
If you are moving forward, you will NOT get into reverse, i'm sure you already know that... And like said before, the layshaft may be spinning from viscous friction or from previous momentum... because the reverse gear has no way to synchronize the layshaft to the speed of the output shaft, you WILL experience a grind if your layshaft is still spinning... also, if you are moving, and the layshaft is not, you will grind as well.... a synchronizer corrects that in the other gears by making the shafts catch up to speed before the gears engage...
another reason you may grind... is because reverse doesn't engage the same way as the other gears.... like said, all forward gearsets are always engaged to the input shaft, and will spin according to the engine/clutch... and are connected to the layshaft through the dogs which are always connected to the output shaft and are selectively connected to the forward gearsets which are constantly spinning in their corresponding speeds... BUT... the reverse gearset is NOT always connected, and has no dog to connect it... instead... there is one gear always connected to the output... one gear always connected to the layshaft... but the two gears are not connected to each other... there is a third gear in this gearset... it is called an idler gear.. instead of a synchronized dog transferring the torque to the shaft... the idler gear is slid in between the two gears on the layshaft and the output shaft... if there is ANY movement in the layshaft while you are stopped.. you WILL hear that gear grind as it tries to mesh between the gears... that is also why a reverse grind sounds different from a forward gear grind... one is a gear physically grinding... one is a dog coming in from the side.... this third "idler" gear is also how the rotation of the shaft is reversed.. each gear in series of a gearset spins in the opposite direction of the previous... all forward gearsets have 2 gears connected... the reverse gear, having 3 gears, obviously spins the output in a direction opposite of the others
one last thing... that is also why it is common to hear a "whirring" noise while in reverse... the forward gears are helical cut, therefore called helical gears... the teeth are cut at an angle, so there is always more surface area of more teeth connected at all times... the reverse gear, in order to slide in to engage, has to be straight cut, called spur gears... a helical gear will smoothly make gradual tooth contact as each tooth comes in and out of contact... a spur gear will "slap" teeth into and out of contact...
So... again... it is very common, and expected for reverse to grind.. it doesn't mean anything is going wrong.. it just means that it is getting old, but still working... every manual vehicle i've ever had ground into reverse... i ALWAYS go into a forward gear before going into reverse... when you are going into reverse, you should be stopped, which means the output shaft is not spinning... no matter what ratio a gearset is, if you synchronize the layshaft to the 0 rpm output shaft, the layshaft will stop spinning... this is utilizing other synchronizers to allow the reverse gear to shift in smoothly, because both gears that the idler has to slip into will be stopped
did i make any sort of sense? i hope i helped...
here are some helpful pics to show you...
here you can see the input shaft (top left), layshaft (bottom), and the output shaft (top right)... you can tell the reverse gear by its spur cut rather than the forward gears which are helical cut... you can also see the idler gear on its own shaft which will slide left to mesh into the two other spur gears to engage reverse...
http://static.howstuffworks.com/flash/transmission.swf
or you can click here to see how it all works... you can shift through the gears to watch how they all engage