Yes, check your ECU harness for oil in the first instance.
www.discovery2.co.uk / Workshop /Injector Harness
I replaced mine as a matter of course when my injector no.1 failed recently. (And obviously replaced the incector too!)
Failed injector will show up as an open circuit fault on the appropriate cylinder, will clear on restart but re-fault. Should be logged historically.
Mine only mis-fired once warm, if that helps with your diagnosis.
Good luck,
James