Looking at https://en.wikisource.org/wiki/Template:Aligned_table which says the syntax is

{{Aligned table
| whatevercolumn1
| whatevercolumn2
}}

Your example in https://en.wikisource.org/wiki/User:ShakespeareFan00/Aligned_table_test is

{{aligned table|cols=3|style=border-collapse: collapse; width: 100%;
|row1header=yes
|nofooter=yes
|Session and Chapter.
|Title.
|Short Title.}}
|}

so there is some unrelated last line.

Sounds correct to display |} as it's not part of anything before. Whether it should be above your table headers instead of below is a question though.

In general, please provide 1) Steps to reproduce, 2) actual outcome, 3) expected outcome in tasks.
See https://mediawiki.org/wiki/How_to_report_a_bug . Thanks!

Thanks, that provides an explanation, but doesn't resolve the issue...

I made an even more minimal example..:-

{|
<tr><td>1</td></tr>
|}

{|
<tr><td>1</td></tr>
</table>

<table>
<tr><td>1</td></tr>
|}

The resultant output being:

<div class="mw-parser-output"><table>
<tr><td>1</td></tr>
<tr><td></td></tr></table>

<table>
<tr><td>1</td></tr>
</table>

<table>
<tr><td>1</td></tr>
<tr><td></td></tr></table>
</div>

Which are all nice and clearly balanced... I fail to see how the parser can handle it in the simple example, but not with the template, when it's an equivalent technique.

You will also note in the first and last examples the generation of additional spurious rows.

Given that aligned table, should be generating appropriately balanced HTML, I fail to see why the parser correctly reads the mixed synatx in one instance and not with the template. Consistency of behavior would be appreciated.

My text example (link earlier) generates :-

<div class="mw-parser-output"><table style="border-collapse: collapse; width: 100%;"><tr style="vertical-align:top"><th scope="col">Session and Chapter.
</th><th scope="col">Title.
</th><th scope="col">Short Title.</th></tr>
<p>|}
</p></div>

What it should be generating (or could have reasonably expected to generate) is:-

<div class="mw-parser-output"><table style="border-collapse: collapse; width: 100%;"><tr style="vertical-align:top"><th scope="col">Session and Chapter.
</th><th scope="col">Title.
</th><th scope="col">Short Title.</th></tr>
</table>
</p></div>

The line feeds are expected given the layout in the source (tiresome but a different issue.)

(Of course if Mediawiki had PROPER suppport for multi-page continuations, and more explictly defined/doucmented whitespace handling, issues like this one would not arise, I've mentioned this previously, with little apparent impact.)