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A rather difficult one in my mind, but we'll see what you can come up with:

Herge was rather proud of his accuracy and even foresight in the science of his adventures. However, error invariably crept in. Name at least three scientific errors in the two moon trip books.

I came up with three, but there very well may be more. I will accept any well reasoned argument for something I have not thought of. And as a clue the three errors I am thinking of are in Explorers on the Moon -- I have included the other book because there very well may have been some I didn't think of.

Do you mean pure scientific errors or scientific-technical errors. I mean a "technial error" could be a different technical solution in real Apollo-voyages. Actually Herge's solution is not then a scientific error just different solution to a technical problem. And I found some pure scientific errors according to nowadays theories, but those weren't errors in Herge's time.

Notable failings include the representation of the Earth as seen from space (there are no clouds), and the lunar landscape, which is represented as craggy, unlike the smooth, undulating hills of reality. The asteroid Adonis is a real object, but despite being classed as a near-Earth asteroid, its orbit does not bring it between the Earth and the Moon.

The books shows gravity being generated through the constant acceleration of the moon rocket. This is unrealistic for two reasons. First, even the most powerful rockets conceived of by science cannot produce sufficient sustained thrust. Second, if the spaceship truly was accelerating at such a rate, the flight time to the moon would be a matter of hours, not days as depicted in the English version of the book. (In the French version, however, flight director Baxter calls the landing site shortly after the rocket has taken off from the Moon to inform them that it will arrive 'in four hours.')

The three that I am thinking of:

One is impossible under physics
One is factually wrong
One is so completely unfeasible under modern technology that even a Cuthbert Calculus would not be able to solve that problem and the ramifications it would have.

Other things under these three categories can be counted - except the things Calculus actually invented, that is, the nuclear motor and calculon.

One more thing-
Well, two-

If it was a nuclear motor, then Archie & Tinny Poo would receive radioactive poisoning when they were out of the rocket near Adonis.
Adonis would not have a sufficient amount of gravity pull to lure Archie to it.
Third, they'd all die of G-Forces when the rocket made those 360 degree turns and other sharp turns.
Fourth, their helmets are clear. They should have been tinted, or else they would have been blinded if the sun was anywhere in their peripheral vision.
Five, there would be no ice on the moon.
Six, Snowy would NEVER have been allowed to join them.
Seventh, the characters would have been floating around the ship the entire trip.
Yeah, I know I said two more reasons, but...

That's good, and I'll give you the point. Just the three I had in mind -- two of them, you came up with, sort of -- the turning of the rocket around like that while continuing movement in the same direction without tearing the ship apart or killing the people inside is physically impossible -- it would be impossible to accelerate at a speed high enough to simulate gravity as it was happening on the rocket without an immensely powerful engine (Herge is actually somewhat consistent on this one, as Tintin & co. make it from the moon to the earth "in a few hours" -- but like I said, the engine would have to be so immensely powerful there's no room for it on the ship) -- also, the clouds are somehow missing from the earth when seen from the moon.

Your turn, go ahead.

Oh, I thought maxmordon scored. Could you, Mark, comment maxmordon's answer? Yes there are clouds, but the other points.

If Adonis doesn't exist between the moon and the earth, it is one correct answer. And the travelling time is another. And... :)

One is so completely unfeasible under modern technology that even a Cuthbert Calculus would not be able to solve that problem and the ramifications it would have.

When Tintin creates that device to blow up the first rocket to stop it falling into foreign hands. That would be impossible because the only way to contact it would be by radio signal.

I know this isn't a complete answer; I'm not after a point

motheroftintin, they have found ice on the moon in recent years. Hergé was proved prophetic on that one.

Mark Falconer, like tuhatkauno, I thought that Maxmordon gave more than enough right answers (lack of clouds, lunar landscape too craggy, incorrect position of Adonis, impossible gravity generation/inconsistently slow rocket speed). What was wrong with his answers?

I thought that Maxmordon gave more than enough right answers

I agree. I believe Mark Falconer may have been confusing motheroftintin's answer as a second attempt by Maxmordon.

Anway, a point to Maxmordon and question setting duties.

Note we have some threads regarding the science in the Moon books should anybody wish to expound further:
Scientific research behind Tintin's Moon adventures
Destination Moon: post launch trauma
Explorers on the Moon - ice on the Moon?