Most first manuscripts are rejected for reasons that have nothing to do with the writing, and several of them are completely avoidable. These are the ones that appear most often, roughly in order of how much damage they do.
Hiring an illustrator
The biggest one, and it's expensive.
If you're submitting a picture book to agents or publishers and you are not an illustrator yourself, do not commission artwork. Publishers choose and pair the illustrator — it's one of the main things they do — and a manuscript arriving with illustrations attached is usually declined on sight.
People spend real money on this before anyone tells them. Submit the text alone.
Illustration notes everywhere
The related error. Manuscripts arrive with bracketed directions on every line explaining what the picture should show.
A small number of notes are acceptable where the meaning genuinely depends on something not in the text — an illustration that contradicts the words for comic effect, for instance. Beyond that, they signal someone who doesn't understand that the illustrator is a storyteller too.
Rhyme, when it isn't ready
Covered more fully elsewhere, and it belongs on this list. Rhyme is where debut manuscripts most often fail technically, because metre problems are invisible to the author and obvious to everyone else.
If you're committed to rhyme, have someone else read it aloud cold. Where they stumble is where it doesn't scan.
Writing to teach something
A manuscript built around a lesson tends to have no tension, because the ending was decided before the character existed.
Not reading current books in the category
The most consequential and the easiest to fix.
A great many submissions are written from a memory of children's books from thirty years ago. Picture books have got shorter, the language has changed, and what was acceptable in a 1980s text often isn't now.
Read thirty recent picture books in your category — recent meaning the last three or four years. It will change your manuscript more than any advice in this article.
Too long
Nearly all first picture-book manuscripts are too long. Cutting a 1,200-word manuscript to 600 is normal and almost always improves it.
Submitting too early
The first draft is not the submission. Agents and editors remember manuscripts, and a resubmission of the same project after revision is a harder sell than a first submission that was ready.
Submitting everywhere at once
Research who actually represents or publishes your category, and send to them. A mass mailing to every agent in a directory is identifiable and ignored.
Paying someone to read it
A legitimate agent does not charge a reading fee. Neither does a legitimate publisher.
Paid editorial services exist and some are genuinely useful, but they are a separate thing from representation. Anyone offering to represent your book for an upfront fee is not an agent.
Giving up after ten rejections
Ten is nothing. Plenty of now-established children's authors collected dozens, and rejection at the query stage usually carries no information about the manuscript at all.