Can a cheap power meter be a good power meter?

The fundamental flaw seems to me is that your fitness level is a really big variable over time between the power your legs are creating and the heart rate it's measuring. As you get fitter you will be producing more power for the same heart rate etc so I'm not sure how it would deal with that, other variables like temperature would also throw it out.

I saw something the other day that may a better fit for you but I'm buggered if I can find it again. It's a speed/cadence sensor (ant+ or bluetooth) with a matching iphone app that translates your wheel speed and acceleration into power once you have told it the model of trainer you are using. At lease it's measuring a real output but it obviously wont work outdoors

Ok - so I speak with a bit of experience here, as both an athlete and a coach to some excellent, highly motivated, riders.
As an athlete, I have owned Powertaps, SRMs, and also my current set-up which is a Lemond Trainer with their 'Power Pilot'.
As a coach, I need all of my riders to have access to some sort of power meter twice a week. I really battle to understand how measurement is accurately and consistently performed without power. The key is that it must be the same one, in the same set-up. Your point about it being consistent is key.

It really doesnt matter what % +/- of inaccuracy they have - as long as its always the same. A good illustration would be the Powertap hub. It works really well on the road. However, put it on a turbo trainer, and the way the frame 'clamps' the rear wheel means that the reading go mental - as the pressure on the axle messes with the accuracy. In that sense, its very hard to use consistently.

From a performance improvement perspective, I used to have athletes using power meters for all their sessions - religiously. I was also the same. I found it ultimately to be detrimental to their performance. It removes any pleasure from riding at all, and makes you a complete loner with your training. I could go into greater detail on this, but its probably not appropriate here. I have now moved to two highly structured sessions per week using power (both of which can be performed indoors - as they are up to 2hrs long), one using heart-rate, and then rest using 'feel' - which is derived from learning 'zones' in the power based sessions.

Ultimately, power measurement is about testing, setting zones, working to them, then re-testing. You just need a consistent place to measure / test, work-out, and then re-measure.
Wind trainer with power, Lemond with power, Ergo of some sort, Wattbike - they would be my suggestion. If you really want to, get an SRM - dont complain when it creaks though....

But it also works on speed so shouldn't it be able to tell you're getting fitter as your speed would be higher for the same HR and cadence etc?
@ Ants, two structured sessions a week sound good as I find it hard to be anymore strict with my regime because I'm a self employed tradie I never know what my hours are and sometimes if I've been up and down ladders all day or bent over digging holes I just can't be bothered doing a hard session the next morning. Another reason I havn't got a PM yet is the fact you mention "stationary trainers". I bloody hate them with a passion and only use mine to flush my legs through after hard rides or light load spins before big races.
Can you get the same benefit by finding a good peice of quiet road and doing intervals on that or are the efforts you do on a trainer a bit long or to precise for the open road?

Ants, 3 hours on the trainer, that's dedication+

I saw something the other day

@Danny
This is probably what you saw: http://www.trainerroad.com

Don't have anything like centennial park on the northern beaches where you can wind it up and not have to worry about stopping. Best I get in that sense is from Mosman to church point along the beaches, steady climb up to terrey hills then another long flat section back to Mosman along Forest way and Wakehurt pkwy. Sometimes you get lucky with the lights and get a good run.
Still , 3 hrs and six bottles on a trainer = wet floor or a laundry full of smelly towels!

I like to slot 1 training session per week as a session on a stationery trainer. It is a drag but the road never matches the consistent power required on a stationery trainer. The other benefits of the trainer are that I don't have to set the alarm to 5 am and if the road is wet I can still get a good session in.

Keep in mind that for me the limitation is skills - how can you spend enough time on the mtb trails when you live in the inner west? I get beaten all the time by riders who live close to the trails but pay no attention to the scientific training stuff (maybe they also aren't 45).

Yes I have the Jet Black. It does the job but from what I have heard the Kurt Kinetic is probably the best trainer on the market.