I just discovered a scenario in which alternating between two watches can be problematic, specifically if you're dieting using an app like LoseIt that gets active and resting calorie information from the Apple Watch.
For the past month or so I've been carefully logging what I eat, making sure to stay below my daily calorie limit. A few weeks ago I had an instance where the next day the app showed me as having busted over my limit even though I was sure I hadn't. Didn't think much of it until it happened again a day or two ago. That time, the entire week's worth of entires were suddenly all about 200 calories higher than they had been before. Did some digging, and found that the discrepancy was with the daily estimated resting calories having retroactively dropped from the 1900s to the 1700s for each of those days. Furthermore, I realized that this happened shortly after I swapped from my 44mm Series 5 to my 40mm Series 4 (to do some yardwork).
More investigation revealed what had happened. In the resting energy data sources in the Health app, you can prioritize the sources so that when information from multiple sources is available (in this case, two Apple Watches), the higher one on the list takes priority. Now, it appears that when you are not actually wearing a watch (such as overnight, if you don't do sleep tracking), it estimates the resting calories as a set number (about 70.5 in my case), while when your actively wearing the watch during the day, the resting calories vary (averaging about 81.5 for me).
So what does this mean? As soon as I put my Series 4 on (which hadn't been worn all week), suddenly it's fixed 70.5 per hour resting energy rate recorded over the past week took priority and overrode the figures recorded by the Series 5 I had been wearing. The solution, for a case like this where one watch is worn almost all of the time, and another is only worn occasionally and briefly, is to set the more commonly-worn watch to a higher priority, so that this would have less of an effect. But it would seem that for someone who regularly alternates between various watches, this could be more complicated to figure out. Admittedly, this is an edge case that is not going to significantly affect many people, but it's just something to be aware of.
TL/DR: having multiple Apple Watches can cause erroneous resting energy numbers to be used in the Health app and other apps.