I recently bought a 1998 ZR600 EFI and I am having problems. It starts great and idles fine but when I apply gas it backfires, cuts out and acts very erratic. I changed the plugs and put fresh fuel in the machine with no improvement.

I have taken the sled to the local Arctic Cat dealer and they have reported that they believe that I need a new throttle assembly. They tested compression and the motor appears strong. They indicate that the cost will be $ 1700.00 for the new throttle assembly and they indicate that it has to be purchased as a package. They also indicate that there is no guarantee that the problem will be resolved after they install it. I know "####" about snowmobiles and hope there might be a "grey beard" in the crowd that can suggest an easier fix.

I note that the previous owner has bypassed the "kill switch" and I wonder if this may reflect that he has attempted to repair the throttle switch?

try unplugging the kill switch. There is a plug under the handle bar cover between the foam. It sounds like the throttle position sensor to me, if it starts up and you are able to get it to drive, you can cut the wire to the sensor, and it will run fine, or sometimes you can replace a couple of washers in the throttle assembly that activate the throttle position sensor. Hope this helps, good luck.

I doubt it is your Throttle body assembly. But, it could be a number of things.

Possibly a broken reed valve, Kill switch circuit as mentioned above, fuel pump problem, or a bad stator.

How do your plugs "read"? Is the problem only with one Cylinder?

The problem sounds like the typical TSS malfunction (Throttle Safety Switch). A malfunctioning TSS will cause an intermittent spark interruption at speeds above engagement RPM. that will result in loss of power and backfiring. Bypassing the TSS will disable the kill switch, but that can be overcome and the kill switch restored and the little switch in the throttle block still bypassed. This sled has the open ignition, I believe, and simply unplugging the three prong connector near the base of the handle bars should eliminate the TSS and kill switch. The root of the problem is commonly the little switch in the throttle block that is activated by the sideways movement of the throttle pivot pin when first pushing the lever. The fix for that is to replace the seals on the throttle pivot pin. Less than two dollars and a couple minutes. #8 in this diagram.
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You may want to look for worn, or broken wires coming from the TPS on the throttle bodies. I've heard reports from people of wires rubbing through near the steering shaft.