In order to answer this question, I have to first clarify that I don't believe in dating just for the purpose of dating. If I did, then I probably wouldn't carry this line of thought with me. I believe that dating or courting (semantics in my opinion) ought to lead somewhere...otherwise, imo, it's pointless. I would never date someone if I already KNEW that it was going to lead nowhere. To me that would be a waste of time and I might be blocking my opportunity to meet my mr. right by spending time with mr. ain't-gonna-quite-cut-it.
I know it's unpopular to say that you would date with the goal of marriage but that's what I believe in. If some people date with the goal of bedding a lot of people and that's okay, I don't see why me wanting the opposite should be 'not okay' (not saying anyone said it wasn't). Anyway, if you're dating towards the goal of marriage, (for me) I wouldn't recommend dating more than one person at a time.
These are the issues that I feel can stem from it. I may like more than one man and have trouble deciding between them. I may compare them to one another, and that isn't fair for me or for my dates. Each of us has to be looked at on our merits. What I can forsee happening and I've seen it with my friends is that that they end up with no one because they think, "Well, he's okay, but the next person may be even better."
A lot of people believe that they will know if someone is right for them very soon. I don't believe that though (although obvious red flags need to be adhered to). Very few people have an instant connection. Movies have taught us to look for that "love at first sight" but it's not very realistic. From experience, I can tell you that the majority of now-happily married couples gradually developed their emotional connections over the length of their courtships. When someone juggles more than one dating partner at a time, they tend to rush to judgment too quickly and give up on a promising relationship simply because it isn't moving as fast as they (mistakenly) believe it should.
Another problem with dating more than one person is that you don't devote the emotional energy and time that is needed to enable a a true relationship to develop. I believe that if a courtship seems promising, the partners should concentrate their energies into getting to know each other well and building an emotional connection.
My life is chaotic enough; another dating partner in the picture is too distracting and confusing.
Finally, I think that it can also backfire when one or more of the people someone is dating, each of whom is probably concentrating on developing the relationship and believes you are doing the same, then discovers what is going on. I realize people well say well...you should have sorted that out in the beginning but I just think it can cause great emotional anguish, as the person feels "two-timed" even if they technically weren't. The person is not likely to tell you that out of the 5 people they are dating you rank 3rd on the list...
Anyway, those are my biased opinions...as usual...