However, if I play through the whole scenario - enter a query into Google, seeing my ads, clicking on my own ads, perform the task on my site which leads to a conversion - I don't see the conversion code displayed on the page! The Javascript-code is embedded in the page, and I did everything a visitor has to do to count as conversion, but I don't see anything!
Of course this makes me think that probably not all conversions are counted?
To determine the issue, you can goto the page with the conversion code on it - then change your settings, refresh the page, and see if 'site stats by Google' shows up. If you don't see the conversion box, change settings again, repeat.
Thanks for pointing me in the right direction!
P.S. Does that mean as a consequence the actual conversion numbers are higher? And the more technologically advanced visitors you have on your site, the less accurate the conversion counters are?
In markets where webmasters/savvy interent users are the primary target, Google conversions are commonly off 20-40%.
In b2b markets that have a good IT department (i.e. the IT staff is running spam software, corporate firewalls, etc) the numbers are usually off 10-30%.
In b2c markets where you're targeting 'joe user' the numbers are usually less than 10% off.