Picric acid forms crytalline derivatives with amines, many phenolic ethers and some aromatic hydrocarbons. Taking the melting point of picric acid derivatives was one common means of qualitative organic analysis back in the days before instrumental analysis.

Vogel (3rd Ed.) lists the melting points of several dozen phenolic ether picrates including those of safrole, iso-safrole, anethole and veratrole.

As Osmium mentioned, trinitrobenzene and styphnic acid were also used for the same purpose.

Styphnic - that's trinitrocresol, right?

Monograph number: 9026
  Title: Styphnic Acid. 
  CAS Registry number: [82-71-3]
  CA name(s): 2,4,6-Trinitro-1,3-benzenediol; 2,4,6-trinitroresorcinol;
  Additional name(s): 2,4-dihydroxy-1,3,5-trinitrobenzene. 
  Molecular formula: C6H3N3O8
  Molecular weight: 245.11
  Composition: C 29.40%, H 1.23%, N 17.14%, O 52.22%. 
  Literature references: May be prepd from natural sources, such as Pernambuco wood extract or quebracho extract by the action of nitric acid:  Einbeck, Jablonski, Ber. 54, 1086 (1921).  Prepd industrially by first sulfonating, then nitrating resorcinol:  Merz, Zetter, Ber. 12, 681, 2037 (1879); Datta, Varma, J. Am. Chem. Soc. 41, 2043 (1919).  Prepd by nitrating 2,4-dinitroresorcinol:  Kametani, Ogasawara, Chem. Pharm. Bull. 15, 893 (1967).
  Properties: Hexagonal yellow crystals from dil alc.  Astringent, but not bitter taste.  Solvated crystals from acetic acid.  Sublimes in high vacuum.  Becomes almost colorless upon vacuum sublimation, but turns deep yellow on contact with air.  When dry, mp 175.5 deg; also reported as mp 179-180 deg.  One gram dissolves in 156 ml water at 14 deg, in 88 ml water at 62 deg.  Freely sol in alcohol, ether.  Acid to litmus.  Dibasic acid.  Deflagrates on rapid heating.
  Melting point: 175.5; 179-180

  USE:  Has been used in the manuf of explosives. 

So the forming of the picrite,in the ref, was just to provide further varification of the product and was not really nescesary to the synthesis.?
VL_

Is this SeO2 demethoxylation a known reaction of some sort? Or is it an oddity?

VL_  Yes, picrate was for ID/analytical purposes.  If you check the archives, I posted an article here a while back on making picrate phenol ethers - "Compound ID for the Hack"

Rhodium: Maybe the reaction doesn't work...the mere fact that it was published in the journal, does not mean it is set in stone.

I guess we will have to find out.  Osmium mentioned it, you found it.  Now Vl needs to have it tested. can methyl iodide be used to remethylate the 4 position.
VL

I forgot where I read it last night, but I found an article where a propenylbenzene was oxidized to the corresponding cinnamaldehyde during alcoholic reflux with SeO2 for a few hours, I wonder if that is a general side-reaction.

That would be an acceptable side reaction.Mabyee with a longer reaction Asarone could be reduced all the way to 2,5 Dimethoxybenzaldahyde Then make the nitrostyrene and reduce it to the amine with Zinc/HCL.  A 2-CB synth for chromic
VL_

Will the aldehyde side product be extracted from the mix with DCM. Will it be in solution in the alcohol. An the SnO2 It must be filtered after an initial H2O flooding correct. Swip was going to flood the mix with H2O, filter the SnO2 off then extract with DCM and distill. After the propenalbenzene comes over then could the 2,5 DMB side product be recrystalized from the distilling flask for later use. If it doesn't get extracted with the DCM then could the rxn mix be concentrated to recover the aldehyde.
VL_