Updated Solution
After some time, I have gotten the bibitem highlighting to work in an acceptable manner. The code below differs from the previous version(s) in that many macro names have changed and the structure of things has been a bit more refined to make this easier for someone else to use in their own work. Specifically,
- The field which contains the infobox text is customizable with
\def\notefield{annotation}.
- You must explicitly name the entries for which you would like to have infoboxes appear. If you opt to include an item for which
\notefield is empty or nonexistant, the bibitem for that entry will still be highlighted, but no infobox will appear.
- Colors and styles for each aspect can be controlled separately.
- References to "Important" have migrated to "Infobox"
Result
The example code now runs with biblatex-examples.bib for a bit better look.

Code
The example bib-file biblatex-examples.bib has many entries; with the annotation field filled for every entry; the vazques-de-parga entry also contains a note field, so you can see what happens when you change the \notefield from annotation to note. Comments related to this are interspersed in the code below.
\documentclass[]{article}
% Set page geometry - this adds a bit more room for the marginpars to live comfortably
\usepackage[includemp,marginparwidth=4cm,reversemarginpar]{geometry}
\newlength{\innermarginparwidth}
\setlength{\innermarginparwidth}{\marginparwidth}
\addtolength{\innermarginparwidth}{-1em}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Load packages
\usepackage{tikz} % Tikz basic
\usetikzlibrary{tikzmark} % Gives \tikzmark for markers
\usetikzlibrary{calc} % Node position calculations
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% User Customizable Options
%
% Some basic options for biblatex
\usepackage[backend=biber,sorting=nyt,style=ieee]{biblatex}
%
% Load bibliography
\addbibresource{biblatex-examples.bib} % Load some examples
\def\notefield{annotation} % Set the bibentry-field that contains your notes---could also be "note"
%
% Set colors & style
\definecolor{InfoboxBackground}{HTML}{F6F6FF}
\definecolor{InfoboxFrame}{HTML}{000077} % Remove frame by making this the same as background
\definecolor{InfoboxText}{HTML}{4444FF}
\definecolor{BibitemText}{HTML}{000077}
\definecolor{BibitemHighlight}{HTML}{FFFF00}
\def\bibitemstyle{\bfseries\color{BibitemText}}
\def\infoboxstyle{\slshape}
\def\infoboxsep{6pt} % inner margins of box
\def\infoboxrule{1pt} % width of rule around box
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Setup Infobox
\DeclareBibliographyCategory{UseInfobox} % Make a category for entries that should have infoboxes
\newbibmacro*{infoboxnote}{\printfield[infoboxnote]{\notefield}} % New bibmacro to print out the infoboxnote-styled note
\DeclareFieldFormat{\notefield}{} % Disable printing of \notefield in other ordinary circumstances
\DeclareFieldFormat{infoboxnote}{\marginpar{\fboxsep\infoboxsep\fboxrule\infoboxrule\fcolorbox{InfoboxFrame}{InfoboxBackground}{\parbox[t]{\innermarginparwidth}{\color{InfoboxText}\infoboxstyle\printfield[labelnumberwidth]{labelnumber} #1}}}} % Insert \marginpar with note
% New \highlight command for bibitem highlighting
% Takes parameter {entrykey} to make \tikzmark pairs unique
% \highlight command should appear before the text to highlight so it is set behind
\newcommand{\highlight}[1]{%
\begin{tikzpicture}[remember picture, overlay]
\coordinate (begin) at ($ (pic cs:#1beg) + (-.5ex,2ex) $);
\coordinate (end) at ($ (pic cs:#1end) + (0,-.8ex) $);
\coordinate (penult) at ($ (begin |- end) + (0,-.5ex) $);
\coordinate (right) at ($ (begin) + (\linewidth+1ex,0) $);
\fill[BibitemHighlight] (begin) -- (right |- begin) -- (right |- end) -- ( begin |- end) -- cycle;
\end{tikzpicture}}
% Set the \tikzmarks ; Place the infoboxnote ; set style for bibitem
\AtEveryBibitem{%
\ifcategory{UseInfobox}%
{\highlight{\thefield{entrykey}}\tikzmark{\thefield{entrykey}beg}\usebibmacro{infoboxnote}\bibitemstyle}%
{}}
\renewbibmacro*{finentry}{\finentry\tikzmark{\thefield{entrykey}end}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
% Identify the entries you want to have an infobox
\addtocategory{UseInfobox}{bertram,sarfraz,vazques-de-parga} % Add items that you want to have infoboxes for
\nocite{bertram,sarfraz,companion,knuth:ct,kullback,wilde,vazques-de-parga}
% Example of \highlight command with regular text to demonstrate how things work
% Note that command highlights with rectangle starting where text starts; indentation not supported
\noindent\highlight{UNIQUE}\tikzmark{UNIQUEbeg}This is a line that goes all the way to the end and has a tikzmark that marks the ultimate end on the next line.\tikzmark{UNIQUEend}
\printbibliography
\end{document}
Original Post
This does everything you want using biblatex... except for the (background) highlighting of the bib-entry (this is particularly hard to accomplish while keeping the ability to have multi-line entries).
The solution uses \marginpar to set the note field of an entry in the margin. As written, you just need to add a note field to an entry; when the note field would normally be set (you must be using a style that wants to use the note), the note is placed in a \marginpar and the entry itself is added to the important category. Every important entry is then typeset in a special font (here, bold and colored).
The other way you could approach this would be to manually specify which entries you'd like to highlight (with \addtocategory{important}{paperA,...}) and removing the corresponding code from \DeclareFieldFormat{note}{...}. Then you could maintain notes with all important papers, but only include the most important ones (or those for which you have space).
The solution appears as:

\documentclass[]{article}
\begin{filecontents}{\jobname.bib}
@inproceedings{paperA,
booktitle = {Proceedings},
year = {2003},
author = {Alpha, Author},
title = {AAA Title of Paper},
note={This paper is of special significance},
}
@inproceedings{paperB,
booktitle = {Proceedings},
year = {2002},
author = {Bravo, Author},
title = {BBB Title of Paper},
note={This paper is also of special significance},
}
@inproceedings{paperC,
booktitle = {Proceedings},
year = {2004},
author = {Charlie, Author},
title = {CCC Title of Paper},
}
@inproceedings{paperD,
booktitle = {Proceedings},
year = {2001},
author = {Bravo, Author},
title = {DDD Title of Paper},
}
@inproceedings{paperE,
booktitle = {Proceedings},
year = {2001},
author = {Bravo, Author},
title = {BEE Title of Paper},
}
\end{filecontents}
\usepackage[svgnames]{xcolor}
\usepackage[includemp,marginparwidth=4cm,reversemarginpar]{geometry}
% Some basic options for biblatex
\usepackage[backend=biber,sorting=nyt,style=ieee]{biblatex}
\addbibresource{\jobname}
%% Highlight entries
\DeclareBibliographyCategory{important}
\DeclareFieldFormat{note}{\addtocategory{important}{\thefield{entrykey}}\marginpar{\printfield[labelnumberwidth]{labelnumber} #1}}
\AtEveryBibitem{%
\ifcategory{important}%
{\bfseries\color{Maroon}}%
{}%
}
\begin{document}
\nocite{*}
~ % Type something....
\printbibliography
\end{document}
Edit for More Color:
You could add a bit more color by using a \colorbox for the note itself:

\usepackage{xcolor}
\definecolor{ImportantBackground}{HTML}{FFE3D6}
\definecolor{Important}{HTML}{A13506}
\usepackage[includemp,marginparwidth=4cm,reversemarginpar]{geometry}
\newlength{\innermarginparwidth}
\setlength{\innermarginparwidth}{\marginparwidth}
\addtolength{\innermarginparwidth}{-1em}
% Some basic options for biblatex
\usepackage[backend=biber,sorting=nyt,style=ieee]{biblatex}
\addbibresource{\jobname}
%% Highlight entries
\DeclareBibliographyCategory{important}
\DeclareFieldFormat{note}{\addtocategory{important}{\thefield{entrykey}}\marginpar{\fboxsep6pt\fcolorbox{ImportantBackground}{ImportantBackground}{\parbox[t]{\innermarginparwidth}{\color{black}\printfield[labelnumberwidth]{labelnumber} #1}}}}
\AtEveryBibitem{%
\ifcategory{important}%
{\bfseries\color{Important}}%
{}%
}