Table - longer numbers

• The particle $M_1$ is actually placed correctly at the moment. (Recall that whitespace padding at both edges of the table is suppressed, courtesy of the @{} particles.) It's the \mc{($ {\rm M_{\odot}}$)} item that is not placed correctly. Just as you did for the case of

  \multicolumn{1}{c@{}}{$M_1$}
  

  you have to write

  \multicolumn{1}{c@{}}{($(\mathrm{M}_{\odot}$)}
  

  in order to get the placement just right.

  Note that {\rm ...} is badly deprecated in LaTeX documents. Don't use is. Intead, write \mathrm{...}.

• The d column type is meant to be employed if the numbers in the column need to be aligned on their decimal markers. If that's not the case, you shouldn't even be using the d column type. You haven't provided much information about the actual types of numbers that may occur in columns 2 and 3. Absent more specific information, all I can assume is that simple centering (via the c column type) is fine for these two columns.

\documentclass[12pt,a4paper]{report}
\usepackage[czech]{babel}
\usepackage[margin=2.5cm]{geometry}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern,textcomp}
\usepackage{amsmath,amssymb,bm} 
\usepackage[nottoc]{tocbibind}
\usepackage{icomma,dcolumn,booktabs} 

\newcommand{\mc}[1]{\multicolumn{1}{c}{#1}}
\usepackage{tabularx,ragged2e} 
\newcolumntype{d}[1]{D{.}{,}{#1}}
\newcolumntype{L}{>{\RaggedRight\arraybackslash}X}
\begin{document}

\begin{table}
\setlength\tabcolsep{3pt} % default: 6pt
%\footnotesize % Don't use footnotesize unless you want to make the material difficult to read
\begin{tabularx}{\textwidth}{@{} L cc d{2.3} d{2.3} *{4}{d{3.2}} @{}}
\toprule
Zdroj & $P$ & $T_0$ & \mc{$e$} &
\mc{$\omega$} & \mc{$i$} & \mc{$a$} & \mc{$a$} &
\multicolumn{1}{c@{}}{$M_1$} \\[0.33ex]
& (dny) & (RJD) & & \mc{($^\circ$)} & \mc{($^\circ$)}
& \mc{($\mathrm{R}_{\odot}$)} & \mc{($\mathrm{M}_{\odot}$)} & \multicolumn{1}{c@{}}{($\mathrm{M}_{\odot}$)} \\
\midrule
Bla bla bla bla bla bla 
& 5,732436(15) & 54002,780(46) 
& 12.345 & 12.345 & 123.45 & 123.45 & 123.45 & 123.45\\
\bottomrule
\addlinespace
\multicolumn{8}{@{}l}{\footnotesize\textit{Pozn:} $^a$ Směrodatná chyba odhadu metodou Monte Carlo.}
\end{tabularx}

\caption{Maximálně věrohodné odhady v~modelu M.}\label{tab03:Nejaka}
\end{table}

\end{document}

I suggest using siunitx, which covers much more than dcolumn does.

\documentclass[12pt,a4paper]{report}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[czech]{babel}

\usepackage[margin=2.5cm]{geometry}  % choose suitable text block parameters
\usepackage{lmodern,textcomp}

\usepackage{amsmath,amssymb,bm} 
\usepackage[nottoc]{tocbibind}
\usepackage{booktabs,siunitx} 

\newcommand{\Mo}{\mathrm{M}_{\odot}}
\newcommand{\Ro}{\mathrm{R}_{\odot}}

\begin{document}

\begin{table}
\footnotesize

\begin{tabular*}{\textwidth}{
  @{\extracolsep{\fill}}
  l
  S[table-format=1.6(2)]
  S[table-format=5.3(2)]
  S[table-format=2.3]
  *{5}{S[table-format=3.2]}
  @{}
}
\toprule
Zdroj & 
{$P$} & 
{$T_0$}  & 
{$e$} &
{$\omega$} & 
{$i$} & 
{$a$} & 
{$a$} &
{$M_1$} \\[0.33ex]
  & {(dny)}
  & {(RJD)}
  & {} 
  & {(${}^\circ$)} 
  & {(${}^\circ$)} 
  & {($\Ro$)}
  & {($\Mo$)}
  & {($\Mo$)}   
  \\
\midrule

1 & 5,732436(15) & 54002,780(46) & 12.345 & 123.45 & 123.45 & 123.45 & 123.45 &\\

\bottomrule
\addlinespace
\multicolumn{9}{@{}l}{\textit{Pozn:} $^a$ Směrodatná chyba odhadu metodou Monte Carlo.}
\end{tabular*}

\caption{Maximálně věrohodné odhady v~modelu M.}\label{tab03:Nejaka}
\end{table}

\end{document}

Note that \rm has been deprecated for more than 20 years. The correct syntax is \mathrm{M}_{\odot}, but I added a couple of new commands for ease of input.

See also Slovak (and Czech) babel gives problems with cmidrule and cline for problems with \cmidrule.