There’s no “right” way to write a letter of intent. Applicant evaluators are so widely varied, you can’t possibly write the ideal letter unless you happen to A) know the evaluators and B) apply to only one institution. Fortunately, there are some “wrong” ways to write a letter of intent. Let’s try to avoid them.
First think from the evaluator’s perspective. They have a monumental challenge- reviewing possibly several hundred applicants for a handful of positions. It is a grueling, churning, time-sucking task that they get very little thanks for. If you give them the opportunity to rapidly assess your letter as representing someone who is not a good fit, it saves them the trouble of reading your CV and letters of recommendation and thus saves them time.
Here are the rules to keep your letter from getting tossed into the discard pile.
One page or less. I know some evaluators read two page letters. I know more who use this as an instant rejection. You should be able to express yourself succinctly.
Good grammar and spelling. This may seem obvious, but I would say a full 20% of letters I read fail this test. Have other people go through your letter _carefully_ with a fine-toothed comb and make sure they are brutally honest.
Good use of English. This one is hard for non-native speakers, but it is very obvious when it is present. If your English is good but not native, find several native speakers to review and correct it. We use language in odd ways in English. The Japanese small old car is technically correct, but does not sound the same as the small old Japanese car.
Avoid a TOO-unique letter. You can and should write your own letter and not a form letter, but if your letter is quirky or eccentric, this may work for some evaluators but not for others. This is highly polarizing with people who feel very strongly on both sides. Don’t risk it.
Don’t use odd word choices, or excessive Thesaurus use. This may not get you an instant rejection, but it can be off-putting. Keep it simple.
Don’t be boastful or arrogant. I think there is some advice out there on the internet that you need to be assertive and confident in your application letters. Maybe this is true for business, but it is not true in academia. Some people may not notice or care about this, but I know many evaluators who react poorly to arrogant letter-writers and veto their application.
As noted in the introduction, evaluators are an extremely heterogeneous group, and you can’t possibly avoid all pitfalls of all evaluators. Maybe some don’t like anything other than a five-paragraph-essay format. Maybe others will reject any letter with the word “yellow” in it. It’s impossible to predict all the things on which evaluators may reject you. However, the tar pits listed here are the most prominent, consistent, and important. Write your letters accordingly and, if you need help, please reach out to me. What elements of letters of application have you seen or heard of which you think should be considered mistakes?