I mean, of course, the final thoughts I'm going to write about verse for a while. There's certainly a lot more that can be said about writing in verse -- probably more that should be said -- but this is all I have to say for the time being.
And these thoughts apply equally well to writing easy readers in prose. It's just that some problems pop up more frequently in verse than in prose.
For example, it's more tempting to write filler words in verse than in prose. The driving rhythm of the verse can distract you from writing simple sentences, mainly because you get too caught up in "How can I make this sentence fit this rhythm?" You start writing bad sentences to keep the rhythm.
Instead, you need to rethink your sentences so that they sound more like normal speech while keeping the proper rhythm. Sometimes that takes a lot of time and effort, but you need to put it in if you want to write good verse. You shouldn't write "I think I would like to go" just because it fits the verse rhythm if you simply mean "I'm going."
Likewise, your characters should not like Yoda talk if Yoda they are not. Just because such phrasing was acceptable 200 years ago doesn't make it acceptable now. In an easy reader, you need to make the sentences sound as normal as you can. Don't write awkward sentences just to fit rhythms or make an easier rhyme.
And make sure your verse can be illustrated. Yeah, I know that isn't always possible. But often you just need to put a bit more thought into your verse (or prose) to make it more visual. Young children are limited in their ability to think abstractly. (I'm not saying that they can't, just that they can't do it as well -- or for as long -- as adults.) You need to make your sentences as direct and easy to understand as you can if you want children to enjoy your stories.
Finally, realize that good verse is harder to write than good prose. This should be common sense, but verse often sounds simpler because of the way good verse rolls off your tongue. If you want to write good verse, it's going to take you longer to finish a story than it would if you simply wrote it in good prose. That's because you have to juggle more balls to make simple verse that sounds better than simple prose. If you aren't willing to put in the time necessary to create good verse, then stick with prose. There's no shame in admitting that you don't want to put extra time in on your work just to get a rhyme. It's all about the story, not the form that the story takes. Write in the form that you most enjoy writing.
After all, if you don't enjoy writing it, the kids won't enjoy reading it. So whether you decide to write in verse or prose, have fun doing it!