Bug 53191

The effect is reproducible with parallel installation of Master "LOdev  3.7.0.0.alpha0+   -  ENGLISH UI / German Locale  [Build ID: b45834b]"  {tinderbox: @6, pull time 2012-09-13 00:10:35} on German WIN7 Home Premium (64bit).:
When I have some short lorem ipsum text and insert a footnote, the footnote anchor is superscript as expected, but the Footnote Character in the footnote area is "normal height". 

At least for German (and may be English) texts I do not think that that is a bug. Although I am used to see footnote characters in superscript, I found various hints that it is common sense that footnote characters should be in normal height, for example in 
<http://www.google.de/url?sa=t&rct=j&q=footnote%20numbers%20(without%20full%20stop%20or%20bracket)%20in%20the%20footnote%20are%20not%20given%20in%20superscript%20form&source=web&cd=1&cad=rja&ved=0CCIQFjAA&url=http%3A%2F%2Fwww.gottfried-wilhelm-leibniz-gesellschaft.de%2FDokumente%2FGuidelinesStudiaLeibnitiana.pdf&ei=zkBXUN3CLIqH4gSIxYG4CQ&usg=AFQjCNH6imGa6FHlZNc3e-h9QwsijmCVwg> (search pdf document for "are not given").

This issue might be Language related, I can't tell whether for other languages other typographic rules are valid.

I see the not superscript footnote characters back until OOo 1.1.5, so Version back to first one.

Workaround: If superscript footnote characters  are required simply the character style for footnote characters has to be modified. 

@Urmas:
Can you cite some public typographic rules for your language underpinning need for superscript footnote characters by default?

Anybody here with access to Typographers’ Bible "The Elements of Typographic Style" by Robert Bringhurst (or a similar specialist book)?

http://graphicdesign.stackexchange.com/questions/10892/footnote-typographic-conventions seems to suggest footnote marker should be fullsize (though obviously early days on the question)

Schulmeister teaches us that footnote marker is a copy of a marker in the body text. But that doesn't matter.
What's matter, is that each normal word processor does it this way, except the latest versions of LO.

I don't agree with the premise of this bug or it's use of terms like "should" and "normal word processor". Presumably the latter reference is to MS Word which is full of weird style anachronisms that everyone now takes for granted. I do not believe LO is obliged to imitate everything done in other word processors. Whether a schulmeister (schoolmaster) teaches this or not is irrelevant. There is a wealth of information from style guides that show the use of superscript, in relation to the note identifier in the footnote itself, varies both between guides and according to context. Here are a few of the more prominent ones:

APA Publication Manual 6th Edition 
§2.12, pp.37-38 provides a prescriptive outline but is not clear on how the footnote numeral should be set. An example in Fig. 2.1, p.51 for footnotes for text body (using an Arabic numeral) appears to be raised: ~20% and have a relative font size: ~85% (default in LO is raised: 33%, relative font size: 58%).
In §5.16, p.138 an example showing footnotes for a table (using a lowercase alphabetic) appears to be set raised: ~25%, relative size: ~60%. Superscript settings are dependent on font, so these figures represent my guesses using Times New Roman, Arial, Gentium, and DeJaVu Sans.

Chicago Manual of Style
Fig. 3.13, 3.14, and 3.15 provide examples for table notes (lower case alphabetic indicator) and these appear set raised: 35%, relative font size: 75%. §14.14 provides an example of using notes for citations. Full-sized Arabic numerals are used. §14.43, §14.46, and §14.52 provide examples of using footnotes / endnotes. Full-sized Arabic numerals are used.

The Elements of Typographic Style v3.2 (R. Bringhurst)
§4.3.3, p.69 is titled "Use superscript in the text but full-size numbers in the notes themselves." A magnified example is provided in the margin. I think this is self-explanatory.

While a feature could be implemented to provide the option of using superscript identifiers in the footnote itself I do not believe it is necessary or recommended (NOTABUG). I feel Bringhurst offers sound advice in this area and LO should do what it can to encourage best practice where possible.

I don't care about US standards or recomendations. All available references state that footnote marker both in text and footnote body should be set along the upper line of the line.

I think you are going to have a hard time finding support to get the current default behaviour changed. The burden of proof (i.e., quoting from several internationally recognised style guides) has been on you since comment #1. To add to this, there will always be differences of opinion e.g.,

http://ask.libreoffice.org/en/question/3094/footnotes-how-to-get-not-superscripted-numbers-in/

I made a mistake in comment #5 when I said "While a feature could be implemented to provide the option of using superscript identifiers in the footnote itself ..." As indicated in comment #1 and in the link I have just provided it is *already* possible to separately style footnote / endnote identifiers in the text area and footnote area.

Workaround: Tools > Footnotes/Endnotes... (or modify the default character styles Footnote Character / Endnote Character).

Given that you can create your own templates with the exact style you require, I now definitely think this is NOTABUG.

I would also say that this is not a bug.
You can also easily change the default behavior so that the footnote characters are superscript.

@Urmas: You might of course bring this discussion to the Design Mailing list.