Let us say that a young man gives a young woman a check and says "הרי את מקודשת לי בצ'ק זה כדת משה וישראל " - Does it work? Of course not - you need two witnesses!!! OK - So you have two witnesses. Does it work?
There is a problem that since not every check is honored or is covered, maybe the woman doesn't have סמיכות דעת [trust] that it is a good check and thus she is not married.
Another issue is whether a check is considered money or maybe it is just a document that is used to represent money or an IOU שטר חוב but is not actually money. One cannot marry a woman by giving her a piece of paper saying that he will give her money [עי' אבה"ע סי' כ"ט סעיף ו]. Or maybe it is considered שוה כסף as having monetary value, because one can use a check to make payments etc.
One nafka minah as to whether a check is money or is a שטר חוב is when the check ripped before it was cashed. If it is money - he already paid, so sorry Charlie. If it is not considered actual money but a שטר חוב it must be replaced because the payment was never rendered.
Nafka minah 2: Is one considered a מוחזק In this money as far as the din of המוציא מחברו עליו הראיה is concerned. If it is money then he is מוחזק. If not - then not.
Nafka minah 3: If one bought the arba minim with a check. If we don't consider it money, then no actual kinyan was made, and he is not yotzei [because we require that he own them].
To be continued bl"n.....