Are there any proposals for special parentheses for function arguments? A few times, I wanted to highlight that a variable in the right-hand side of an equation depended on other variable. I can't recall a good example right now, but consider this one:
$\tau = F d(\vec{r})\cos(\theta)$.
Probably, the person who hypotetically wrote probably wanted to mean that $d$ depends on $\vec{r}$. In my experience, many students will think that $d(\vec{r})$ means $d \times \vec{r}$.
That problem would not exist if there were specific parentheses for function arguments.
 A: Yes, there is at least one. Murray Bourne, owner of the site Interactive Mathematics, proposes writing boxed arguments:

I wish to propose an alternative notation for concepts where you cannot expand in the way you do with simple algebra. It might look something like this:
$\sin\boxed{x + y}$
$\log\boxed{x + y}$
$f\boxed{x}$
This would send a much clearer message to students that the particular function or operation does not work in the same way as simple algebra works.

[...]

So a more computer friendly option would be to (exclusively) use [ ] - square brackets - for such concepts, like this:
$\sin[x + y]$
$\log[x + y]$
$f[x]$

http://www.intmath.com/blog/learn-math/towards-more-meaningful-math-notation-661
So, you (I?) weren't the first one to think about it. Those proposals don't seem to be very popular, probably because everybody is very used to $f(x)$, which has a long tradition in Mathematics. Surely, expression like
$f(x+1)(x+1)$
might be confusing, but that problem could be eased by having different space lengths for arguments and multiplicative factors, say
$f(x+1)\, \, (x+1)$,
putting factors always before functions,
$(x+1)f(x+1)$,
which, on the other hand, could make long calculations involving multiple factors less clear if the positions were always rearranged to follow that rule.
One could also always write explicit multiplication symbols:
$f(x+1)\cdot(x+1)$
or
$f(x+1)\times(x+1)$.
Having a consistent notation is also helpful: if an $f$ or a $g$ is also followed by a list of arguments between parentheses, people are less likely to interpret that list as a multiplicative factor.
In your example, you could also write
$\tau = F d \cos{\theta}$
where $d := d(\vec{r})$.
If I recall correctly, there are also authors that use always a special font for the letters representing functions, and others who use small size, vertically centered arguments between parentheses, like this:
$f\vcenter{\scriptstyle{(a)}}$,
so that distinction from multiplicative factors is more evident:
$f \vcenter{\scriptstyle{(x+1)}}(x+1)$.
Someone defined a mathmiddlescript macro for LaTeX that could be used for that purpose:
https://tex.stackexchange.com/questions/250961/subscript-superscript-middlescript
Combining styles, we may have interesting options:
$f\vcenter{\scriptstyle{[x+1]}}(x+1)$
$f\,\vcenter{\scriptstyle{[x,\,y\,|\,a,\,b]}}$
