The obvious danger of a pay to bearer negotiable instrument is that the bearer will not be the intended payee of the negotiable instrument.
A pay to bearer negotiable instrument might take such a form because the negotiable instrument specifically says so, or because the negotiable instrument does not feature any instructions as to whom the payee should be, or even because the negotiable instrument says that it is payable to cash. Any of these circumstances would define a negotiable instrument as a pay to bearer instrument.
Such pay to bearer instruments likely facilitate a greater ease of payment, but they also are much more likely to be misused or lost, as simply losing the physical documentation of the negotiable instrument would be enough to lose the payee all the money of the negotiable instrument.
Pay to order, on the other hand, is made out specifically to a clear person or party. A pay to order negotiable instrument is very much unlike a pay to bearer negotiable instrument in that a pay to order instrument is non-functional until endorsed. Because a pay to order instrument can only be paid to the person cited on the instrument itself, it must be officially endorsed by that person in order to become payable.
A pay to order check or other instrument which is endorsed can, however, functionally become a pay to bearer instrument. Once the endorsement of the party mentioned on the instrument is added to the instrument, if no other instructions were added with the endorsement then it can be used by whomsoever comes to hold that instrument. This is why it is often dangerous to endorse a check immediately and why it makes a great deal more sense to attempt to endorse the check only when actually using it.
Other options include mentioning instructions on the check, such that even if endorsed and lost, the check will at least be limited in its use. Pay to order checks can also remain pay to order if they are endorsed over to another party, with that party then becoming the new order to whom the check will be paid. The newly endorsed party will also have to add his or her endorsement to the check in order to make it active again.