Ten out of ten for some lovely koi including the buterfly, opps thats me drummed out of the British Koi Keepers Society (we dont recognise Butterfly koi as of yet )

no I think they are beautiful but its a US thing at the moment.
Joking aside they are coming from a 26 year veteran of koi keeping.two very nice looking koi .
It could be one of many factors that are resulting in these deformities
1) Food
Perhaps you could augment their diet a little in the summer with some more natural foods as well as pellet (buy an AKCA guide to koi Nutrition), $3.00 AKCA website then try again it may well be they were lacking something
2) Water Conditions
No one has of yet asked you your water perameters Ammonia , nitrite, nitrate, Ph, Kh, Gh did you do something differnt this time to last time everything factors in .
3) Age
It may be that these koi are not yet fully mature this being their first and second spawnings (what size are they), they normally say 10" is the right size to start breeding
I can see no problem with breeding a long fin with a short fin the resulting fry will be a mix but to get deformities like that doesnt sound right it .
4) Differing male koi
I would add another male the next time you breed then see what happens if you get the same result then it has to be a problem with the female
5) Genetic problems
Something Val and I know only too well. Val having Facioscapularhumeral Muscular Dystrophy (we decided against children simply because it wouldnt be fair on any child born with MD ), so its the same in nature ..
It could well be that your fish may look perfect but genetically they are not thus the resulting in the deformities.
It is no secret and is well known that koi only a small gene pool to work from resulting in thngs like the Immune system being deficent, deformaties etc ( I've lost a koi to its immune system crashing ) .
So as you can see you have more than a few things to get right before you get the results that your after , however best of luck with your next spawning ,
Dave