Person A makes Claim X. Person B states Claim X is baseless. Person A then states that at some point in the past, Claim Y would have been considered baseless.

I believe that a look into the pattern of the argument and what kind of fallacies are commonly committed through this pattern is a little helpful.
Let's formalize the argument of person A:
P1: Solving daytime cloud dispersal and nighttime rain to water the plants is something that people have found to be unbelievable when they heard about it the first time.
P2: Speaking into a device in your hand and taking moving pictures and sending them to the other side of the world is something that people have found to be unbelievable when they heard about it the first time.
Therefore: solving daytime cloud dispersal and nighttime rain to water the plants is achievable in the future just like speaking into a device in your hand and taking moving pictures and sending them to the other side of the world turned out to be achievable in the future.
The pattern of this argument is to:
a) State a claim/situation.
b) State another claim/situation.
c) State a common shared characteristic between the two claims/situations.
d) Conclude, based on the common characteristic shared between the two claims/situations, that something else true of the latter claim/situation is also true of the former claim/situation.
Arguments that follow such a pattern are mostly susceptible to either a weak analogy<> fallacy or a false equivalence<> fallacy. If you can point out certain differences between the two claims/situations that show that the two are disanalogous/not equivalent in a way that makes what is true of the latter claim (stated in b) not necessarily true of the former claim (stated in a) despite the common shared characteristic (stated in c), then you have shown the argument to be fallacious.

Person A's second statement is known as the "head explodes" fallacy....because this attempt at rationally assessing what "people" would think a hundred years ago about the world now by traveling back in time to tell them, knowing that to do that you'd need a time machine, sends the statement into "fuse" territory. Then knowing that a time machine existing would negate the ignorance of the future, at least within some people, which then nullifies the whole premise of the statement....this type of reasoning sends my head on a journey that will most likely make it explode...or maybe it's a hyperbole fallacy....but I digress.

I agree w/ all of the comments above. I especially like Skip's "heads explode" fallacy. Interesting.

I suggest that this could also be a simple questionable analogy. Analogies usually make weak arguments, and this one seems weaker than most.

This is the Galileo Fallacy<>, which Dr Bo describes thus:

Claim X is made.
Claim X is ridiculous.
Person A argues that claim Y was seen as ridiculous at the time, and it turned out to be right.
Therefore, claim X is true (or should be given more credibility).

Here's an example:

A: I've made a free energy machine
B: That is impossible - your calculations are probably wrong
A: That's what they said when Einstein discovered relativity

The point is, on very rare occasions in the past, ideas which seemed crazy turned out to be true. But on uncountably more occasions, they turned out to be just as crazy as they seemed. In the Galileo Fallacy the arguer is claiming that, because a true idea was mocked in the past, the very fact that you're mocking his idea, makes it more likely that it's true.