A local company has been advertising continuously for the same job (on Stack Overflow Jobs and elsewhere) as well as periodically advertising for various junior-level jobs for at least a year. Is there a way to know whether this is due to legitimate growth or some other more serious problem (being disorganized in their hiring, overly selective, experiencing high turnover, people being unwilling to take the job after interviewing, etc.)?
Many large companies have generic postings for different teams. For example there might be a web team, a mobile team, an internal apps team and a dev ops team. For entry level positions they're mostly going to be the same. Some coding, some scripting, CS degree helpful, etc.
Also, many shops have hundreds of developers. So, even with low turnover rates they're always looking for new candidates. And some are always willing to pay to keep the door open to rockstars when they come through.
It's unlikely that they've been holding out for 10 months trying to find the right person to fill their team. They're most likely casting a large, wide net.
If you are otherwise interested in the job, you can just apply and ask in the interview, if you don't experience the reason beforehand.
For software developers, which is what it sounds like you're referring to, it just is really hard to find even basically competent developers. The term "negative unemployment" is often used, meaning there are more jobs than qualified applicants. So if you need, say, six developers for a position, it can take a very long time to fill all of those positions, and six isn't that many.
My experience is working in a small contracting company that was constantly hiring (and growing). We contracted to Fortune 500 companies for positions that they were also trying fill with full-time employees of their own. We had difficulty having enough people to fill all their open positions, and they had difficulty filling those positions at all. And this was in the city with the highest number of software developers per capita in the world.
My impression is that the market is out of equilibrium. So besides growth, you do have effectively a bit of being "overly selective" in the form of hiring managers who have a hard time giving someone a $150,000 salary, say, when they have a (genuinely) equally competent employee earning only $100,000. You also have people turning down offers because they over-estimate their own value. They see a market rate of $150,000 and assume that they should get at least that. There is a return on investment for developers, and it varies wildly depending on the quality of the developer. To restate it, employers aren't always accepting of the fact the same quality developer just is more expensive now, while employees are often assuming that they are worth these high salaries just for showing up.
There is no way to tell without inside information.
I know companies who continually advertise for roles on nothing more than speculation and perhaps to keep employees on their toes or some other reason. The roles don't actually exist, they would need to sack someone to open up the position they're advertising for and they haven't expanded in a decade.
Other companies have a high turnover or are expanding and advertise legitimate positions.
There is no way to tell without applying.