First of all. Unless there was a big change recently in Navision that I missed, inventory costing does not get adjusted to Jobs. I think the only way you will get proper costing in Jobs is if you use standard costing. But I could be wrong. (I could be wrong though, since I have not looked at Jobs in great detail in Navision Since about ver. 3.10)
The main effect the Posting Date has in the adjustment routine, is it determines the date that the value entries are updated, which means when filtering, that this is the date that will give you an acurate Inventory Valuation. The most important thing, is to NEVER back date the Inventroy Adjustment date to any date prior to and Purchases or Sales, and prefereable nevre backdate at all unless you are really sure why you are doing it. If for example today is Oct 24, and you want to run this for September. Well if you put in a date of Sep 30, and you had purchases and sales invoices in October, then its possible to get Negative inventory valuations for thos items. Also you can get an item that has 0 on hand, and a positive value on the GL. Of course you can also get errors like this by running the Adjustment process, and then posting back dated Purchase invoices, and running adjustment again.
The key is don’t back date the process.
My recomendation is to run the porcess as often as possible, each night if you can. Ideally just before midnight, and dated to that same day. Then always at the financial end of month, someone else should manually run the process again to make certain that it ran. This way at worst case you are at least able to go back and get an end of financial month inventory valuation.
So to answer your question, the date should be the actual date when you run it. But if you always run it forward to the end of the current financial period, then at least you can get a valid month end report, evne though mid month it will be a bit wonky.