TeX is in a funny state at the start of table cells, it's best to avoid doing anything too clever there and beamer gradual reveals come in that category:-) \leavevmode gets you to a safer place.

\documentclass{beamer}
\usepackage{times}
\usepackage{amsmath,amsthm, amssymb, latexsym}
\usepackage{exscale}
\usepackage{booktabs, array}
\usepackage{graphicx}
\usepackage{setspace}
\usepackage{tabularx}
\usepackage{listliketab}
\begin{document}
\begin{frame}{}
\begin{listliketab}
\storestyleof{itemize}
\tiny
\begin{tabularx}{3.50in}{lXX}
\hline
& Observation & Conclusion \\
\hline
\leavevmode\uncover<2->{1.} & \leavevmode\uncover<2->{Observation 1 } & \leavevmode\uncover<2->{Conclusion 1} \\
\leavevmode\uncover<3->{2.} & \leavevmode\uncover<3->{Observation 2} & \leavevmode\uncover<3->{Conclusion 2} \\
\end{tabularx}
\end{listliketab}
\end{frame}
\end{document}
For the first l column you're not leaving a mode at all (\relax would have done as well) you are just forcing TeX to stop looking for \multicolumn etc. In the X columns you need to stop the look-ahead for spanning columns but in addition you need to start the paragraph so the specials and any other nodes that beamer's magic drops at that position go at the start of the first line of the paragraph and not before the paragraph. You see the same with \color (which is why \textcolor starts with \leavevmode as does \mbox and most other latex commands of this sort.
aligntag as it's reserved for questions related to the environment provided by theamsmathpackage; I also removed the thanks and your signature, as it's always done automatically :) – cmhughes May 9 '12 at 20:36\begin{tabularx}{3.50in}{XXX}then the problem goes away... I don't know why this 'fixes' it though... – cmhughes May 9 '12 at 20:40\begin{tabularx}{3.50in}{p{1cm}XX}and change the1cmto anything you like... – cmhughes May 9 '12 at 21:07