I often wonder about notation and what is acceptable. I have seen many different ways of linking equations together, sometimes with just $=$ and others with $\iff$ or $\implies$. Now, I know when solving a limit or a derivative for example, you can link using only equals signs.
$$ \frac{d}{dx}\left[\frac{x^2}{3x}\right] = \frac{2x(3x) - 3(x^2)}{9x^2} = \frac{6x^2 - 3x^2}{9x^2} = \frac{x^2}{3x^2}=\frac{1}{3} $$
However, when solving a two sided equation then it becomes ugly to use $=$, so I stick to $\implies$ where I have seen others use $\iff$.
$$ \sin x = 1 - \cos^2 x \implies \sin x - (1 - \cos^2 x) = 0 \implies \sin x - \sin^2 x = 0 \implies \sin x(1 - \sin x) = 0 \implies x = n\pi \text{ or } x = 2\pi n + \frac{\pi}{2}$$
Some others seem to think this is abuse of $\implies$, and it should be reserved only for cases such as
$$ \log_b x = y \iff b^y=x $$
When should I use $\implies$ and $\iff$ where it will be accepted by the majority?
I have made the mistake of using $\implies$ instead of the biconditional in the past.
Essentially, if you are trying to show equivalences, then it is a good idea to use the biconditional. Otherwise, users may become confused, because they will interpret it as meaning that the former implies the latter, but not the other way around.
For example, $x = 0 \implies \sin{x} = 0$ makes sense because there are other solutions for $x$. In other words, $\sin{x} = 0 \implies x = 0$ is false.
But if you were to state $x - 3 = 2 \implies x = 5$, you might not be choosing the best formatting, because it's also true that $x = 5 \implies x - 3 = 2$. The statement is not wrong, but it is not as strong as it could be. It leaves it open whether or not $x - 3 = 2$ when $x = 5$.
I think you already knew this. Maybe it is a little anal pointing this out, but if you are going to write something, why not write it properly?