Have you read the codes?
Before replacing parts, check that the response of the sensors is indeed slow or non-existent.
Series II Discoverys log error codes for many reasons. The Service Engine light indicates many different issues that may also indicate transmission conditions (Thanx Mr. Robinson for making this clearer to me and encouraging me to buy the next module for my Rovacom-Lite)
D'Oh, to answer your question directly, if it is in fact due to poor oxygen sensor response, you may continue driving your vehicle with impunity. The only impact of this may be diminished fuel economy and peformance. When the response of the sensors becomes too far out of expected ranges, the vehicles will enter "limp home" mode. You'll be fine!
Peace,
PT