Updated answer, fnpct version 1.x
You can use fnpct. The only thing you need to to is “adapt” \footnotetext so fnpct knows that it should step over it:
\documentclass{article}
\usepackage[dont-mess-around]{fnpct}
\usepackage[colorlinks]{hyperref}
\AdaptText\footnotetext{o+m}{\IfNoValueTF{#1}{#NOTE{#2}}{#NOTE[#1]{#2}}}
\begin{document}
This text has multiple sequential footnotes, but comma delination is disrupted
if one of the footnotes has a nested footnote\footnote{Here is a footnote}%
\footnote{Here is another footnote\footnotemark.}\footnotetext{This is the
nested footnote.}\footnote{Here is the third (non-nested) footnote.}.%
\end{document}


This also works with the option ranges (which do not work well with hyperref obviously:
\documentclass{article}
\usepackage[dont-mess-around]{fnpct}
\AdaptText\footnotetext{o+m}{\IfNoValueTF{#1}{#NOTE{#2}}{#NOTE[#1]{#2}}}
\setfnpct{ranges}
\begin{document}
This text has multiple sequential footnotes, but comma delination is disrupted
if one of the footnotes has a nested footnote\footnote{Here is a footnote}%
\footnote{Here is another footnote\footnotemark.}\footnotetext{This is the
nested footnote.}\footnote{Here is the third (non-nested) footnote.}.%
\end{document}

Original answer, fnpct version 0.x
I recently answered another question and somehow got carried away... anyway, there now is a new package, fnpct, which (by accident, really) offers a solution. Or rather two solutions.
- the
\innernote command
- the
\multfootnote command
The following code shows three working examples and one with a maybe unexpected output:
\documentclass{article}
% the option turns the punctuation switching and kerning adjustments off:
\usepackage[dont-mess-around]{fnpct}
\usepackage[colorlinks]{hyperref}
\begin{document}
% \innernote works well as long as you don't need to nest another level deeper
This text has multiple sequential footnotes, but comma delination is disrupted
if one of the footnotes has a nested footnote\footnote{Here is a footnote}%
\footnote{Here is another footnote\innernote{This is the nested footnote}.}%
\footnote{Here is the third (non-nested) footnote.}.%
% The consecutive placing works well as long as one uses the package option
% punct-after' (or the optiondont'mess-around' which calls the former
% implicitly) but fails otherwise:
\newpage
\setfnpct{punct-after=false}
This text has multiple sequential footnotes, but comma delination is disrupted
if one of the footnotes has a nested footnote\footnote{Here is a footnote}%
\footnote{Here is another footnote\innernote{This is the nested footnote}.}%
\footnote{Here is the third (non-nested) footnote.}.%
% if it is a single inner footnote then \multfootnote works, too:
% place \footnotemark and use the * argument (= \footnotetext) inside
% \multfootnote. In this case the package option doesn't disturb anything.
\newpage
This text has multiple sequential footnotes, but comma delination is disrupted
if one of the footnotes has a nested footnote\multfootnote{Here is a footnote;Here
is another footnote\footnotemark.;*This is the nested footnote.;Here is the third
(non-nested) footnote.}.%
% the combination of both methods is probably best:
\newpage
This text has multiple sequential footnotes, but comma delination is disrupted
if one of the footnotes has a nested footnote\multfootnote{Here is a footnote;Here
is another footnote\innernote{This is the nested footnote}.;Here is the third
(non-nested) footnote.}.%
% so we can see that `hyperref' cooperates well:
\newpage\null
\end{document}
The fourth example looks like this:

\oldfootnotetext[\ref{footnotemark\thefntextcntr}\textsuperscript{,}]{#1}. But probably it won't fix the spacing issue. – percusse Dec 28 '11 at 09:30