Let's break it down. Firstly, it seems the question is unaware of something fairly standard in traditional Judaism, which is Hashem gave the authority to make halachic rulings to the Sages of each generation. He defined what they decree as His will. See Midrash Tanchuma Nasso 29:
A person should not say, "I will not fulfill the commandments of the
elders (rabbis), since they are not from the Torah." The Holy One,
blessed be He, said to them, "My children, you are not allowed to say
this. Rather, observe anything that they decree upon you, as it is
stated (Deuteronomy 17:10-11), 'And you shall do according to [...]
the law that they shall instruct you.'" Why? Because I also agree
with their words, as it is stated (Job 22:28), "You will decree and
it will be fulfilled for you."
Generally, not only does He agree, but He finds their halachic "innovations" more precious to Him than His own laws. See Mishna Sanhedrin 11:3 and discussion there.
It is codified as an actual mitzva of the 613 mitzvot based on the explicit verse in Deuteronomy 17:10 and onwards; the mitzva for us to listen to the Rabbis. See Sefer HaChinuch 495 for example. Note how this creates a logical identity between "Torah law" and "Rabbinic law".
This is the true meaning of Hashem "partnering with man" in the creation of the world. The Chachamim are given permission to take Hashem's Will, and bring it down into the physical world by deciding how His will applies in every detail of the world. The wider discussion behind this would make for its own question, but see "Halachic Man" by Rabbi Soloveitchik for further reading, for example.
To proceed with understanding how this process of Hashem's will being brought into the world can be a flawed process, let's ask a bigger question first. How is it possible for us to sin in the first place? Hashem doesn't want us to sin, it is against His Supreme Will. How can something against His will happen? Did He make a mistake?
The angels certainly accused Him of making a mistake, creating mankind, in the Zohar 1:23a:
Aza and Azael also opposed (man's creation). When the Shechinah said
... "Let Us make man," they responded,
"What is man that You take knowledge of him?" (Tehilim 144:3). Why do
you wish to create man when You know that he shall definitely sin
before you
The short answer is that Hashem's higher/inner will is that we refrain from sin by our own choice, not by force of His will. Us being realistically able to sin is therefore necessary for His inner will (see the rest of that Zohar), no mistakes but exactly what Hashem needed.
It's the same answer here with regards to our case. Hashem wants a relationship with us, and gave us the hands-on study, of learning in order to perform His will. I'll note here that this anecdote is seemingly telling us that it's not Hashem who made a mistake (He doesn't know what He wants?), but our beloved holy sages, which we wouldn't dare say had this story not implied it.
This partnership is a marriage, which means it must be realistically possible for us to make a mistake regarding the correct opinion on a particular halacha, debate it, and end up with a majority wrong, otherwise they are robots, clones of Him, and that's not a marriage, and He is still alone.
Further reading on the nature of free will, and the purpose of it, would be excellent in further understanding the above points.
It would also be prudent for the reader to look into the halachic process, and the history of the Oral Transmission at this point. How can such errors and mistakes arise, how severe are they, what does it mean in terms of whether we are performing Hashem's will or not.
Suffice it to say that for the sake of this answer, whatever the sages decide is more precious and beloved to Hashem than what He would have decided Himself, at least in regards to this halachic decision. This is true even if it is a "mistake", given that the Chachamim are following protocol, and are sincerely trying their best with what they've been given.
The chassidic definition of "good" means "what is important to you
matters more to me than what is important to me", and Hashem is the
ultimate good.
The "what if they made an evil decision" question is a bit more complex. It is theoretically possible, but the systems that Hashem put into place to ensure that this is unlikely. The criteria for deciding our judges, the system of giving authority to older generations over newer ones, the adverserial nature of deciding halacha... This is also a huge topic out of scope for this answer that would be worth reading up on separately.
It also seems, historically speaking, that when the corruption of exile became too much of a problem, the halachic process became more rarefied and less innovative, in order to avoid our knowledge of Hashem's will becoming corrupted too. This occurred thanks to the check and balances given at Sinai, applied by the last of our truly great leaders, and guided by Hashem's Hand of Hashgacha.
The last point about Hashem's Hashgacha is important too. We follow His protocol and try our best, and then say in our prayer "we are fallible and prone to make mistakes, please help us and ensure that we don't destroy your world with the huge responsibility you've given us" and that prayer has been answered. We have made it 3335 years since Sinai, and Hashem has indeed listened to the Rabbis on these matters, yet here we are, keeping Torah and Mitzvot faithfully until this day.
tl;dr: This aggadah does not raise the point of Hashem making mistakes, and certainly doesn't imply that He makes one here. Hashem saying "My children defeated Me" comes with a laugh because it is out of the delight of His inner will, that we precious yet fallible people of His are sincerely trying to know, get close, and fulfil the mission of our God, with our own free will. Definitely not a mistake, but the whole point of creation.
