Why does the arXiv produce a messed-up DVI when the PDF is fine? Historically, I've checked the quality of arXiv output by reading the PDF it creates; I learned today that this actually a serious mistake.  If you look at the PDF and DVI for my most recent article, you'll see that the PDF looks fine, and the DVI is essentially unusable from a mathematical perspective.  The tikz pictures don't come out at all, and there seem to be serious font issues.
I'll note that this file compiles fine as a DVI on my home computer.

What's causing this?  Is it a problem a user can fix by include font/style files with his/her upload?  is there someone at the arXiv I should be telling to install something?  Why is the arXiv less competent than a home installation of MikTeX?


EDIT: So, the take-away seems to be that your DVIs from the arXiv will only look right if you use Computer Modern.  Hooray for all math papers looking the same!
 A: Apparently the source of the problem is that TikZ behaves differently when the TeX file
is compiled with pdftex/pdflatex instead of the standard tex/latex.
Instead of simply embedding PostScript into the DVI file, as any sane system would do,
it apparently tries to draw figures using characters from some special fonts.
In my opinion, TikZ authors should be crucified for this.
Mathematical papers are supposed to last a little longer than 10 or 15 years.
In 10 or 15 years PDF will be replaced by yet another format,
and all TeX files that are tailored specifically for PDF will become unusable.
So long for durability.
For this reason I urge everybody to ignore Andrew Stacey's advice (no offense meant).
One more reason to use METAPOST instead of TikZ.  They seem to have
similar functionality, but METAPOST is much more powerful when it comes to solving
systems of equations, has more convenient syntax (no annoying backslashes),
and is also an order of magnitude more portable (for example, any document with METAPOST pictures looks
exactly the same in DVI, PostScript, and PDF formats).
As for the fonts, we should blame arXiv for this.
The DVI format is device independent.
However, a DVI file must always be accompanied by all fonts that it uses,
except for the standard Computer Modern family.
The arXiv simply gives you the DVI file without any fonts, which I find ridiculous.
Since the paper under discussion uses some weird PostScript fonts,
and the arXiv gives you a DVI file without any fonts,
it is natural that the DVI file is unreadable on many machines.
I apologize for somewhat strong language, but I feel very strongly when
it comes to the issues of portability and/or durability of mathematical papers.
For example, 10 or 15 year old LaTeX files are often no longer compilable on modern TeX systems
and require some voodoo magic on my part, because of the changes in the LaTeX
and its various packages.
For this reason I switched to Plain TeX about 10 years ago.
A Plain TeX file created in 1982 will compile without any errors and will produce
exactly the same document in 2012 or in 2042.
[If I am allowed to comment on the appearance of the paper, I must say
that it looks quite weird with the current fonts.  Apparently, PostScript
fonts are used to typeset the main text, but all formulas are still typeset in Computer Modern.
Since the two fonts are obviously incompatible in style (for example, they have
different thickness), the end result is horrible.  If I were to read this paper,
I would recompile it using the standard Computer Modern fonts.
Again, no offense meant.]
A: Sadly, DVI is misnamed.  It isn't truly "DeVice Independent" as DVIs do not embed fonts.  So to see a DVI correctly, you have to have the fonts available.  This can be hard to debug since if you happen to have the correct fonts on your computer then you won't see a problem.  PDFs, on the other hand, embed their fonts so avoid this problem.
Moreover, as mentioned in the comments, tikz does it's best when exporting to DVI but cannot do much.  If you have complicated drawings, you need to bypass the DVI stage and go straight to PDF.
You could add a remark to the abstract on the arXiv saying "Don't use the DVI version, use the PDF".  If you wanted to be really cunning, you could add some LaTeX code at the head of your document that tests for PDF mode and produces a warning in DVI:
\RequirePackage{ifpdf}
...
\begin{document}
\ifpdf
\else
\begin{center}
\textbf{Warning:} The DVI version of this paper may be corrupted.  If possible, use the PDF version.
\end{center}
\fi

should do the trick.
A: TikZ's DVI driver only supports a very restricted subset of capabilities. As its amazing docs say, "Naturally, very little is possible with this driver."
(I cannot tell from a quick glance what fonts issues there are: maybe you can be more explicit?)
A: Please review section
9.2.1 Selecting the Backend Driver
of the pgf/tikz manual. arXiv dvi is generated with the dvips backend driver, and it must be post-processed with dvips to render in a useful way. In addition all the fonts referenced in the dvi need to be available to dvips when post-processing the dvi.
There is also section 
9.2.5 Producing Perfectly Portable DVI Output
which seems like a choice of last resort.
Cheers
T.
A: It appears that I don't even have a DVI previewer anymore. When I downloaded your DVI file, I renamed it to have a .dvi extension. When I ask OS X Finder to open it, it launches TeXShop, which apparently runs dvi2pdf (or something similar), and then shows me a PDF which looks just fine.
