There is no good reason for bypassing the O2 sensors; without them, the computer operates in open loop with no way to control the air/fuel mixture in varying conditions. Unless you have a wide band O2 sensor wired into the computer, you have shot yourself in the foot.
Dump codes sticky
Look at the top of the 5.0 Tech forum where the sticky threads are posted. One of them is how to dump the computer codes. Codes may be present even if the CEL (Check Engine Light) isn’t on. You don’t need a code reader or scanner – all you need is a paper clip, or if your lady friend has a hair pin, that will do the job.
I highly suggest that you read it and follow the instructions to dump the codes. http://www.stangnet.com/mustang-forums/threads/how-to-pull-codes-from-eec4.889006/
Welcome to Stangnet
I moved your thread to talk. More member traffic through here.
How was the car tuned ?
When you say the O2 sensors where bypassed, do you mean they where deleted with a tune? Or are they just unplugged?
I assume they have been tuned out, not just deleted.
But, as others have said
It will give us internet folks something to start with otherwise we are all just guessing ignition or fuel related....which it could very well be. I'm actually leaning ignition related, and it's possible performing the "cylinder balance test" part of the code reading process would clue you into a particular cylinder that is misfiring.