1 onion and potatoes do not go together.
2 by end spring bed 5 will empty since all three are early crops
3. tomatoes should be on other side of bed assuming the top diagram is north.
4 the corn bed can hold at least 20 more plant
5 did even bother to read book since you missed most of important consideration. when design a planting scheme using the square foot method. all you used is some spacing and ignored most of rules.
go back to drawing board your plan is a waste of the space you have.

if you would like I will revise it for you.

another rude comment by ribsyhuggins

dennis_of_alabama ok you do better. I thought not.

I do believe that Ribsy means well in this situation. At first I was taken aback by how rudely he followed up his advice, but if you read it thinking he has good intentions, he really is just pointing out that there is a lot of wasted space in this example. There have been a lot of other times from what I've seen where he DOES seem purposefully rude so I can't say for sure. Just giving him the benefit of the doubt. :)

I would say, however, that I disagree about planting potatoes with onions. There is no reason why the two shouldn't be planted together.
Here is a really helpful guide I found for companion planting listed below.
http://www.ghorganics.com/page2.html

If your tomatoes are bush tomatoes then there is no need for them to be against the fence, however if it is the case that they are bush types then they may be crowded in their alloted space. If they are vining then either they need more space, or you could put them against the fence and guide them to grow up.

From what I am seeing of your garden layout, you have a whole extra column and row of squares that you can utilize, if your boxes are 4' wide and 6' long. I think it would be helpful if you drew the lines of the squares in, because there IS a lot of wasted space, you could have a much more bountiful harvest then the one pictured. Hope this helps!