One of the opportunities and challenges of Shidduchim is doing adequate and proper research. The cliche and much maligned question of whether the family uses a plastic tablecloth on Shabbos, is not merely urban legend. Whether or not that’s your burning question, it behooves us to discuss what level of research is necessary.
Our Gemara on Amud Beis discusses whether the “checking out” that relatives do is sufficient enough so as not to be concerned if he marries her and finds out she has a deal-breaking flaw. The concern in our Gemara is if she married a cohen, perhaps she should wait until he consummates before she can eat Terumah. This is just in case he discovers that she was hiding some kind of defect that would retroactively invalidate the marriage due to having married under false pretenses. Because certain defects are private and can only be seen in intimate quarters, the Gemara considers if an external “checking out” by relatives is reasonable that we shouldn’t be concerned that there is some hidden defect.
Since our Gemara follows the “Mishna Acharona”, the final version of the Mishna, in a general sense, it comes out in favor of more research. That is, there is a fear that there may be hidden problems. This is not an absolute proof, as the Gemara is discussing fears of being invalidated for Terumah retroactively, which may activate different precautions than standard Shidduch investigations. Nevertheless, it is an interesting point, because had the halacha been in accordance with the Mishna Rishona, it l would have shown less concern about hidden flaws and faults, to the point of not being concerned about Terumah, surely then we should be less concerned about Shidduchim. However, this is not an absolute proof either, as you might argue part of the reason that the rabbis in the Mishna were not concerned about a hidden defect is that they assumed that the research of the relatives (and village gossip) was so effective, that even a hidden fault would come out. So, we cannot prove much about this question from our Gemara either way.
However, there is a responsa of Rav Moshe which speaks clearly to the issue at hand:
"One should not be too clever [in searching for a mate, rather look for] a woman who you find attractive both in her appearance and in [the qualities] of her family, and who has a positive reputation that she follows our traditions. With regard to such a person, you should rely on the above evidence and marry her in the hopes she is the one designated for you by Heaven. It is not necessary to excessively inspect her and such efforts will not accomplish anything...one should relate to Hashem with simple trust (Devarim 18:13)." (Igros Moshe, Y.D. Vol. 1:90)
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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