Altered summary to more accurately reflect the described issues (i.e., not frames). There are two distinctly separate issues reported here related to line border widths and styles: (1) handling of old content via copy / paste; (2) display of the UI line style element being dependent upon line width. Issue (2) would appear to be at least partly related to bug 47194 and may in fact be a duplicate. Comments 2 and 3 in that bug indicate that v3.5 saw a change in the available border widths and styles that affected old (pre-v3.5) documents, which is likely what issue (1) is. 

Dealing with issue (1), in the provided document the original paragraph (circa 2009: OOo v2.4-3.1, with "double line, 0.05 pt") has the XML:

> <style:style style:name="P12" ...>
>    <style:paragraph-properties ... style:border-line-width="0.002cm 0.035cm 0.002cm" 
>    fo:padding="0.3cm" fo:border="1.11pt double #000000" ...

... which is a ~0.06pt line + 0.99pt gap + ~0.06pt line. When this paragraph is copied (v3.6.2.3 is indicated) to the second paragraph example it becomes:

> <style:style style:name="P8" ...>
>    <style:paragraph-properties style:border-line-width="0.012cm 0.012cm 0.012cm" 
>    fo:padding="0.3cm" fo:border="1.05pt double #000000"

... which is a ~0.34pt line + 0.34pt gap + ~0.34pt line, which indicates the visible difference, even at a zoomed level. Conversely, copying the original paragraph under Ubuntu 10.04 running v4.1.3.2 results in:

>    ... style:border-line-width="0.002cm 0.035cm 0.002cm" 
>    fo:padding="8.5pt" fo:border="1.11pt double #000000"

... which is identical to the original. It therefore seems possible that this issue (1) has been at least partially resolved under newer versions although it would be good if this could be confirmed.

(In reply to comment #1)
> >    fo:padding="8.5pt" 

This value in the last example should read "0.3cm" (I copied the wrong piece of code).

(In reply> Created attachment 71802 [details]

REPRO STEPS: downloaded Document where the problem can be seen.
> 
> Frame styles around paragraphs are assigned confusingly and different to
> previous versions. Should work like before.
> Operating System: Windows XP
> Version: 3.6.3.2 release

Able to reproduce running LibreOffice 4.4.0.0.alpha1 on Mac OSX 10.9.5

Copying and pasting old paragraph with 0.5px. double-lined border works. Opening border styles and closing without changes recreates the issue reported above and shown in the attached file. The border shows as a thick single line in the preview (although double-lined and 0.5px is shown as selected). The screen shows ~ 1px thick, single-lined border.