Hey, see my post
http://www.immigrationboards.com/viewtopic.php?t=130546
Basically I had a similar issue but I think mine's worst because it's the SOC code and in the guidance is says that if you want to change the SOC you have to assign a new Cert of Sponsorship.
However, my HR got a wrong info from the UKBA helpline and they said put the amends in the notes section as it will be considered. So my HR just amended and put in the change in the notes section.
My visa was eventually approved. However, unlike your visa validity dates (that will be clearly printed on the BRP - which technically should follow your employment period as per CoS (in your case hopefully the note) +14 days). If they approve yours, at least you will know if they approved it using the correct date or wrong date. In my case the SOC is nowhere to be seen! Only way to check if they approved it with the note or the wrong one is to contact my caseworker, and that is only by post!
So a bit of a hassle, I still am waiting to hear from my caseworker what code he used, whether the one in the notes or the wrong one.
But in your case only three outcome (a) they refuse if putting a note for date change is not acceptable (b) they approve with the wrong date, which you'll find out straightaway when you receive your BRP (c) they approve with the right date, which again you'll know straight based on your BRP.
scenario a) losing a bit more of money - either putting a new application through or through the appeal process (b) can be tricky but I think again would involve writing to the UKBA caseworker - I would think scenario b is a bit dumb for the caseworker as if he knows its wrong why would he approve a wrong date (c) you're sorted!
I think I read somewhere in this forum a guy had his 'start' date wrong on the CoS (instead of end date), but he submitted a change of circumstances form and the caseworker accepted it. Can't find the link, but definitely in one of the first few pages of the Tier 2 forums. Good luck.
I am still waiting for mine, fingers crossed! Hope I helped a bit - maybe not an outcome, but definitely similar situation. Probs worst!