For the grate in an outdoor grill, I think you can feel safe not cleaning it, but only under the following condition: Before each use, you heat the grill to a temperature in excess of 250 degrees (F) for at least 15 minutes. Gotta heat it up to make sure you kill everything that might have got onto it since you last used it.
Since you really ought to heat the grate up pretty seriously before trying to cook on it anyway, this is almost a no-effort thing.
In terms of extending the life of your grate, it's good to give it a good burn-off AFTER cooking if you're not going to clean it outright. Burning off will make sure there aren't any wet or corrosive things still left on the grate.
As to the broiler pan, I would never let that one go unwashed. Unlike a grill grate, you don't preheat it, so you don't have a chance to kill the beasties that might have grown up in whatever you left on it from last time. If you cooked a steak yesterday and didn't wash the pan, the grease and juices have had 24 hours to attract and breed bacteria and whatever by the time you use it today. Then you pull it out, plop another steak right on your bacteria colony, and broil. What's exposed to the heat directly may get hot enough to kill germs, but what's directly under your steak almost definitely will NOT.
Will you get sick if you don't clean your stuff? Maybe not--it's your life. But please, please, please, don't be so casual about cleaning if you're cooking for ANYBODY else. And really, cleaning a broiler pan isn't that hard. You can man up and just do it.
This is quite common and pretty harmless. The scratches you see don't go very deep, nor are they very wide. My All-Clad saute pan is nearing 10 years old and has a ton of micro-scratches on the interior. It still performs beautifully.
That said, the scratches can grab onto proteins and cause sticking. However, this is simple to prevent with both oil and proper pan preheating.
When a pan is preheated properly the metal expands, essentially closing all of the micro-scratches. This prevents the proteins from grabbing onto them and getting stuck. You obviously need oil/fat to assist with this as well.
To properly heat a pan to the appropriate temperature I suggest using the water drop method. If you put a cold pan on heat and drip a drop of water onto it, the water will sit there for several seconds then boil away. As the pan gets warmer this will happen more quickly, fizzling away in a second or so. Once the scratches start to close something weird happens.
First, the drop of water will break into a few mini drops which scoot around the pan as they evaporate. This is a sign that you are almost there. When the drop of water stays whole (mostly) and scoots around the pan like a mercury ball, this is the perfect temperature. I the water instantly vaporizes on contact, you've gone way too far and need to let the pan cool down. At this point you should add your oil/fat, swirl it around, and immediately add your food. (Make sure the mercury ball of water is gone before adding oil).
Also note that the mercury-ball phase is definitely too hot for unclarified butter, and may be too hot for some extra-virgin olive oils. They may instantly smoke upon adding.
Again, it's important to have your oil and ingredients in place (mise en place) before you start. It's quite easy to skyrocket past the mercury-ball phase if you have to open your oil, pour, and then season your ingredients.
Best Answer
The temperature of boiling water is 100° Celsius or 212° Fahrenheit. This is considerably colder than the self-cleaning cycle in your oven. It would be perfectly sufficient to set the oven temperature to about 120°C/240°F to heat the tray. It would not take long to reach the desired temperature for the tray at those lower temperatures since metals conduct heat well.