Well, there's a lot of info supporting and thwarting the case of Anna Anderson. In history, you need to look at both sides or your view might not be correct. I personally shift back and forth in my belief (I seriously have nothing better to do...)
Evidence-Anna Anderson reminded Maria Rasputin of the Red Cross nurse outfit incident and convinced her.
-Anna reminded Gleb Botkin's son about the "funny animals"
-Anna's face, scars, feet, features, ears (specially) resembled that of the Grand Duchess.
-Anna also had the same foot deformity as Anastasia, hallux vulgus.
-Anna recognized people that the genuine Anastasia knew by their voice.
-Anna knew about the peace mission her uncle went on (yes, it was true).
-Also later on it was discovered that the DNA test was not taken %100 correctly.
-There is strong evidence supporting that the DNA test was rigged, by the people who wanted to discredit Anna.
-Anna's ears looked exactly like Anastasia's. No matter what photographs or methods were used the result was the same. The ears were identical.
-(This probably falls under the features point, oh well) Anna had the same mesmerizing eyes, and identical auburnish hair color. (Is auburnish a real word if not it is now!!!

)
-Anna's handwriting was very similar to that of the Grand Duchess.
-According to interviews of some of the executioners, it was declared that Anastasia had survived.
-There is a chance that only the Tsar, Tsarina, and Tsarevitch were killed and the daughters imprisoned somewhere else after their parents' deaths and Anastasia ran away and survived.
Evidence thwarting Anna-Anna read magazines about the royal family.
-Anna had accurate details about the family's bank account (it is highly unlikely that Anastasia would have had this information).
-Anna was "proven" that she wasn't Anastasia through DNA (though after an thorough investigation problems about the test were uncovered).
Anna was probably NOT Franziska. Because
-Franziska's hands were rough while Anna's were soft and well kept.
-Anna could speak many languages that Franziska could not. This was confirmed by Franziska's family.
-Forensic experts found many differences between the two faces.
-Franziska's teeth were like "black stumps".
-Franziska did not have hallux vulgus while Anna and Anastasia did.
-Franziska's siblings met Anna and said she was too polite to be their sister.
-Franziska disappeared in the May of 1920 while Anna was found in February.
-Also if Franziska was admitted to Berlin hospitals and sanatoriums six times by 1920 why did no one recognize Anna?
But then again she could've been
-Franziska's sibling said she did look like Anna.
-Franziska did resemble Anna a bit.
Please visit this website which helped convince me a bit that Anna was Anastasia,
http://www.geocities.com/kransnoeselo/Front.html Anyway, Anastasia was a delightful child and it was a terrible thing that happened in Ipatiev house during the night of July 17th of 1918. Also if Anna wasn't Anastasia, she is still a remarkable person herself. Both deserve recognition. Well, that took a long time to type...At least I have chocolate to guide my way!! MUAHAHAHAHA...I'm not weird, well not a lot...