The subject of grammar in writing is close to my heart. That doesn't mean that I'm some kind of expert, far from it, I frequently make mistakes and have two proofreaders that I rely on to iron out the problems. It is important to get it right for me and I believe that I'm improving.
Our Justice Secretary, Mr Michael Gove, has made pronouncements on grammar to his civil service staff some of which are fundamentally incorrect. For example, he has banned the starting of sentences with the word 'however' and also using contractions such as 'doesn't' instead of 'does not'. In fact because language is a dynamic, living thing that changes and he is harping back to the way he was taught in prep and public school. In a sense he is being a product of his upbringing and you can't blame him for that, but he has no business trying to browbeat his staff to use a style of grammar that was fashionable forty years ago.
In fact there is no rule against using 'however' to begin a sentence but the placing of the comma or even semi-colon is important.
What about the importance and relevance of grammar?
I recently came across an article by Tomasz P Szynalski saying that we shouldn't rely on grammar rules and he gave very good reasons.
For example native English speakers will say,
'Look at that big, red car.' rather than 'Look at that red, big car.'
In fact this habit of native speakers encouraged the linguists to produce a rule that describes the order in which we place adjectives. Briefly, the rule describes that when more than one adjective is used to describe an object they appear in a specific order.
opinion adjectives: general/specific
descriptive adjectives: size/age/shape/colour/nationality/material
Szynalski goes on to say that asking why a rule exists is asking something that is impossible to answer. His premise is that rules were written as a result of observing the habits of native English speakers.
This position also supports the dynamic nature of language and so Mr Gove my message to you is leap into the 21st century and respect where your staff are in their language development.
In fact several famous authors abused the rules. Mr Dickens wrote run-on sentences; Jane Austen double negatives; and, William Faulkner took liberties with capitalisation and began sentences with conjunctions. The point is that their stories were good and the grammar anomalies of lesser importance. So if you worry too much about whether you have written something badly, it is good that you care, but be kind to yourself and remember you could be beginning a new grammar rule.