Can we set properties to establish a valid asset per field? Craft will let us define what file-type is valid for a given asset field, but there are many times where I'd like to enforce other properties too - e.g., a minimum dimension for valid images uploaded to that field (i.e., dimensions must be larger than 800x600). Is there a way to do that? 

Currently I can only see Craft enforcing file-types and file-size limits if they're too large (e.g., 4Mb is too big). I'd like some more options to avoid clients uploading unsuitable files.
Currently, no. The only file-based validation Assets fields have right now is the type. If you want to enforce a certain size, you can do that on the template end using image transforms. I would suggest adding some instruction text to your Assets field that provides a minimum suggested size, and note that smaller images will be scaled up and look gross.

That said, if you really want to enforce a minimum width/height, or other properties, you can do so by writing a plugin that provides its own field type, which extends AssetsFieldType and overrides its validate() method with your custom validation:

public function validate($value)
{
    // Let AssetsFieldType do its validation first
    $errors = parent::validate($value);

    if (!is_array($errors))
    {
        $errors = array();
    }

    if (is_array($value) &amp;&amp; !empty($value))
    {
        foreach ($value as $fileId)
        {
            $file = craft()-&gt;assets-&gt;getFileById($fileId);

            if ($file)
            {
                if ($file-&gt;width &lt; 600 || $file-&gt;height &lt; 400)
                {
                    $errors[] = Craft::t(
                        '{filename} must be at least 600x400px.',
                        array('filename' =&gt; $file-&gt;filename)
                    );
                }
            }
        }
    }

    if ($errors)
    {
        return $errors;
    }
    else
    {
        return true;
    }
}