If I could suggest some critique...
Kotagaeshi...having broken ukes posture why give it back to him? look..uke is bent over then he is standing straight again.
Irimi nage...check out http://www.kyushinkan.com/
...Its been posted under Peter Browns introduction and shows how this version of irimi nage can be countered with sutemi waza. Further to this...Ukes striking hand remains free - If it contains a knife then it can simply be withdrawn to rip ukes guts out. Finally the irimi nage seems to function solely by applying a forearm smash to ukes neck.
Generally very effective until you meet the no necked monster that every dojo has.
Far better to break ukes balance from the rear. Otherwise for me it is force against force, yang against yang...and not particularly aikido.
Ushiro Waza. No. I can say nothing more that that. Can anyone believe it is good martial arts practice to present your rear to an uke in the hope that he takes your wrist.
I did think the sentiments expressed were very valid and in his way the instructor presented a good selection of aiki . Obviously everyone here practices differently and usually they have a reason for the way they do things. So I don't want to be overly critical.
Hopefully my comments are food for thought...if there are responses then I will learn from them.