Gary,
I realize that you are new to aikido, but if I may lend you some discernment, this video shows a fairly common problem with aikido randori. The uke make their attacks sequentially 95% of the time. They are providing opportunities to complete techniques that probably shouldn't be there. It basicly amounts to a series of one-on-ones that has nothing to do with controlling multiple attackers.
On the other hand, when uke attack simultaneously they will put a great deal more pressure on nage and create much more interesting situations. Techniques will have to adapt accordingly.
There are numerous instances in this short video, but 0:08 and 0:21 are the most illustrative. If the uke were acting together nage would likely have been smashed both times. At 0:31 uke do attack simultaneously, noticeably changing the "effectiveness" of nage's response, but they lack the intention to bring nage down.
Also, while I doubt that punching at a moving target is great idea, I know kicking at a moving target is a bad idea!
Out of curiosity, I searched YouTube after I wrote this post. Here were the first three videos that came up and a related video. They feature a 2nd kyu, presumably some dan-ranked practioner, and a 7th dan all showing the same problems.
http://www.youtube.com/watch?v=FpujsGWRkn4
http://www.youtube.com/watch?v=vtm0HOGFK9w
http://www.youtube.com/watch?v=KoziYiw7W1U
http://www.youtube.com/watch?v=XFz_L...eature=related (What was the significance of adding a fourth uke? Did it change anything other than giving more rest to the uke between attacks?)