I replaced the 4500-mile old 108 link KMC chain that came on my bike with a 110 link Dura-Ace chain. The KMC one was stretched a bit so that it was almost as long as 109 Dura-Ace links. I'm running a compact double (50/34) in front and a 11/27 cassette in back. Should I remove two more links from the Dura-Ace chain, or is there nothing to worry about?

I think you will be okay, but I wouldn't bother to count links. I always use Sheldon Brown's big-big+1 method.

+1 on sheldon brown,

unless your derailleur's bottom pulley is rubbing the bottom of the chain when your in the higest gear, if that makes sense. you should be ok.

Despite a long standing respect for SB, I have always used Shimano's recommendation of largest chain ring - smallest rear cog - derailleur pulleys line up perpendicular to the ground that comes packaged with its derailleurs. It has never failed me. In this system the chain is threaded through both derailleurs when the measurement is established unlike with Sheldon's system. I can see how the Shimano recommendation might not work so well for a very low (largest) rear cog, but as I say, I have used it up to 28 on a short cage RD without fail.

The problem with the Shimano method is the pulleys may always be off vertical - angled a little backward with a slightly long chain and a little forward with an inch shorter chain.

Campy's method recommends the longest possible chain that will never need to be lengthened if a cassette with a larger cog is added later. Thread the chain through the RD and put the chain in the little/little combination. Make the chain as long as possible - just long enough to swing the lower jockey pulley forward when the ends are brought together. Also be sure that the chain dues not rub on the pulley cage. The only time this method does not work is with a setup that exceeds the RDs wrap capacity.

The big/big plus 1 inch method gives the shortest possible chain. Users also need to know that if the ends of the chain that are brought together when wrapping the big/big are the same and can't be joined, then you add 1-1/2 inches or 3 links to get the minimum length. This is the best method to use if the setup exceeds the RD's wrap capacity, but would also result in the chain hanging loose when using the little ring and some of the smallest cogs.

Not sure what "big-big+1" means, but the chain does get very close to rubbing itself near the lower pulley on the RD, so maybe I should take another two links out. Wished I would have known about that before I removed the links becasue this will cause me to use the spare pin that Shimano provided with the chain (and they don't recommend breaking the chain in the same place).

Well that is true, but I have never had it cause a problem. If it is tilting very slightly to the rear, that would be a chain a little on the long side, to the front would be a chain slightly too short. As you say you want to choose the length for which one more or less link makes the two pulleys point the other way. Depending upon your philosophy you can choose which one you prefer. The same thing happens with all chain fitting methods. For example in the largest-largest+1 method, the fit isn't exact either in most cases, but if you insist the chain must come together and have no separation, you will almost always be a little long. You don't allow it to be a little short. So with Shimano you could achieve the same thing by always having the pulleys either perfectly vertical OR slightly pointing down to the rear. No real difference there.

https://sheldonbrown.com/derailer-adjustment.html#chain

Note that if you swap cassettes or wheels (I have crit wheels (11-23) and climbing wheels (12-28), for example), size it with the cassette with the biggest big cog.