Does a perfectly price discriminating natural monopoly cause externalities or any type of market failure? In perfect price discrimination, all mutually beneficial trades take place, the natural monopoly captures 100% of the surplus, and pareto efficiency is achieved. 

However, I've read various sources that mention that, despite this, economists still advocate various taxes, regulations, or nationalization to "fix" the monopoly problem even in theoretical cases of perfect discrimination. Why would these things be advocated if pareto efficiency is achieved? 

The only thing I can think of is that, while the lack of competition doesn't remove the incentive for a monopoly to innovate, it hugely slows down the rate of innovation, which would essentially rob society of potential improvements. 

Is there anything to this logic? What inefficiency would exist if not pareto inefficiency?
The question seems to be in between theoretical model and reality. In one type of theoretical model one may argue for the monopolist, in another against him. In reality it is worthwhile to mention that no monopoly can achieve first degree price discrimination. It is barely theoretically possible and not technically feasible. Other forms of price discrimination do not necessarily yield Pareto-optimal outcomes. Real world economists usually argue against monopolies in general, not against theoretical first degree price discriminating monopolies.

Even if there were such a monopoly there is an answer to "Why would these things be advocated if pareto efficiency is achieved?"

There may exist a multitude of Pareto-efficient allocations. A rather usual consideration for any social planner is some sort of fairness (or envy-freeness, or inequity-aversion, etc.)

In a setting corresponding to a monopoly with first price discrimination as you say all the surplus is captured by the monopolist. This is such a distribution of surplus/goods/utility that it will probably not meet any of the usual fairness criteria.

So while the monopolist might create an efficient allocation of goods, the allocation might not, and usually will not, meet secondary criteria deemed desirable by society.