Given the new frugality, they will recruit on their own rather than contract with an executive search firm for many of the positions and assignments under-$100,000. So, there is plenty out there to analyze in terms of competitive intelligence.
To begin with, the writer of the ad might gush about the strategic direction and strengths of the company. Read between the lines and you can learn quite a bit.
If the gush is too intense, for example, the company may already be in trouble or headed there. The ad is a come-on to attract talent to a distressed enterprise. On the other hand, if things are sweet, then to ensure receiving applications from top folks in the field they will give some details about where they are strategically and operationally. Since you are in that industry, you know what to drill down to.
Then there is the matter of tone. If they are addressing applicants like dirt you can be nicer and poach incumbents. Should they be too much into being a fun bunch, then you can put out there the ethos of being all-business and earning a ton of money.
A tip-off that the company has internal problems is the ad being posted too often. A book publicity agency in Fairfield County, Connecticut has the same ad on Mediabistro.com every six months. You can put in a sly comment to a client or prospect about the unfortunate high turnover at the competitor.
No, companies don't have to identify themselves. You just know.