Hi loobyloo, to give it it's full name to confirm I've got the right one; Photinia fraseri 'Red Robin'
This should be looking at it's best at this time of the year, with the young leaves tinged with red.
If the brown spots are mainly confined to the tips of the leaves, then it's probably just a bit of winter damage which it should hopefully recover from.
If the spots are small blotches all over the leaves, then it sounds like a fungal attack which can be controlled by spraying with a coper based fungicide or Dithane 945.
Good Luck Tbird+
Ps You should be able to pick up a spaygun at your local garden centre.