Can you refresh a single module/chart without refreshing the whole dashboard?

Yep, it can be done if you're using the advanced XML.

I cant think of an app offhand that does it but im sure there is one. You just put a SubmitButton module into the XML as follows:

Example:
1) an ordinary dashboard panel in the Advanced XML, with no SubmitButton

<module name="HiddenSearch" layoutPanel="panel_row1_col1" group="No SubmitButton.. :(" autoRun="True">
  <param name="search">* | top sourcetype | fields - percent</param>
  <param name="earliest">-30s</param>
  <module name="HiddenChartFormatter">
    <param name="charting.chart">bar</param>
    <param name="charting.primaryAxisTitle.text">Sourcetype</param>
    <param name="charting.secondaryAxisTitle.text">## of events</param>

    <module name="FlashChart">
    </module>

  </module>
</module>

2) same panel, but with a SubmitButton

<module name="HiddenSearch" layoutPanel="panel_row1_col1" group="with the SubmitButton :)" autoRun="True">
  <param name="search">* | top sourcetype | fields - percent</param>
  <param name="earliest">-30s</param>
  <module name="HiddenChartFormatter">
    <param name="charting.chart">bar</param>
    <param name="charting.primaryAxisTitle.text">Sourcetype</param>
    <param name="charting.secondaryAxisTitle.text">## of events</param>

    <module name="SubmitButton">
      <param name="label">Refresh</param>

      <module name="FlashChart">
      </module>
    </module>
  </module>
</module>

Make sure that the module tag for the SubmitButton encloses the FlashChart module and also that it encloses any other modules that will be displaying data for this particular job -- most typically headers. As is always the case with the containment of module tags, if someone isnt enclosed by a module, then they know nothing about that module. So in this example if a SimpleResultsHeader is not enclosed by the SubmitButton, then it wont be refreshed when users click on it.

Another option is to add a custom module to splunk that can refresh periodically. Let's call the module AutoRefresh. To do this you have to create the following directory structure (in an app, eg. search or better a custom one):

$SPLUNK_HOME/etc/apps/someapp
| - appserver
   | - modules
      |- AutoRefresh
        | - AutoRefresh.conf
        | - AutoRefresh.css
        | - AutoRefresh.js

AutoRefresh.conf:

[module]
className = Splunk.Module.AutoRefresh
superClass = Splunk.Module
description = This module refreshes it's descending modules periodically.

[param:invervalInSeconds]
required = True
label = This parameters defines the inverval in seconds in which the descending search modules should be reloaded.

AutoRefresh.css:

div.SplunkModule.AutoRefresh { display: none; margin: 0; padding: 0; }

AutoRefresh.js:

Splunk.namespace("Module");
Splunk.Module.AutoRefresh = $.klass(Splunk.Module, {
    initialize: function($super, container) {
        $super(container);
        var interval = (+this._params['invervalInSeconds'])*1000;
        this._timer = setInterval(this.refresh.bind(this), interval);
    },
    refresh: function() {
        this.pushContextToChildren();
    }
});

Once you've added those folders and files you have to restart Splunk. Then you'll be able to use the module in your advanced xml views like this:

... truncated ...

<module name="GenericHeader" layoutPanel="panel_row1_col1">
    <param name="label">Status</param>
    <module name="AutoRefresh">
        <param name="invervalInSeconds">10</param>
        <module name="HiddenSearch" layoutPanel="panel_row1_col1_grp1" autoRun="True">
                    ...
        </module>
    </module>
</module>
...

In this example all (search-)descendants of the AutoRefresh module would be refresh every 10 seconds.