This is an overview question on Halokhos of Kiddushin in general.
Many many ways of Kiddushin result in "Kiddushin in doubt" ("מקודשת מספק"). Examples:
- Omitting "to me" in "Harei At Mekudeshet..." renders a marriage "in doubt" (Sho"A EH"E 27)
- One who says to a woman, "You are hereby betrothed to me with this coin, from now and for after thirty days," and someone else came and betrothed her within thirty days, she is doubtfully betrothed to both of them. (ibid 40,3)
- If he betrothed her with food or a vessel or something like this that is worth less than a perutah, she is doubtfully betrothed (ibid 31,3)
We know that we should make effort to minimize Mamzerim and illicit relations, therefore we should prefer rendering a marriage invalid in case of doubt, than declaring it "Married in doubt" and allowing further Mamzerim in doubt etc.
Another reason is to "Stay away from doubt" (Mishna Avot 1, 16).
We have two rules that would eliminate a great part of those doubts: one allowing the Sages to override Torah's rulings altogether (e.g. rendering Torah's "Kinyan Kesef" invalid), second to make use of "כל דמקדש אדעתא דרבנן מקדש" - All marriages are subject to Rabbinical approval. They could either render all cases of doubt as invalid a priori, or set clear rules for Kiddushin to eliminate the doubts. For example instead of doubting wether a woman understood what's been said and agreed to it, the Sages could demand from her to rise or clap her hands twice.
However they did not use it at all (only one case of Gerushin returning his Get).
I'm aware of the discussion on what Torah rulings the sages are allowed to render invalid (like "בשב ואל תעשה"), but many agree that, just like in Kinyan case, they could do it in Kiddushin.