As any writer will know they are not the best person to look for any errors or omissions in their work. Read it through certainly pick up some obvious mistakes of course. However being too close to your writing is one of the reasons that book editors exist and of course the same applies to essay writing.
As an essay writer your main task is to research and develop a coherent argument within the quite formal structure of an essay. Grammar spelling and punctuation are extremely important when writing an essay on a subject which calls for good language skills - English Literature for example. However an essay on other subjects also needs to adhere to similar grammatical standards. The rules of grammar exist for a positive purpose such as ease of communication and to avoid ambiguity not simply for some arcane reason lost in the mists of time.
Having enough to say If your child is still stuck find out if they have read up enough on the topic. Some inertia with writing can be due to lack of knowledge. They will find writing so much easier if they spend another day or two reading more on the topic and gleaning some additional ideas. Try using a neutral sentence Suggest starting the essay with a neutral sentence: a sentence that merely states an interesting fact on the topic being written about. Heres one: Mozart was one of the most important Austrian composers of the eighteenth century. First sentences in essays dont need to be stellar - you just need to start!