That's not completely unexpected:  BMWs always read high, although rarely
that high (there are some regulations that mandate higher-than-actual
readings.)
My '01 330xi reads around 2mph high at 60mph, and our '91 525i reads about
the same.

I've checked the speedo using my GPS, radar warning signs along the road,
timing, and comparisons with other cars.  I've also asked Garmin, and they
believe that their GPSs should be +- 0.5mph or better, IIRC.

FloydR

In BMW's I have had (4) the speed warning device is 2-3% high and the speedo
5-7%.  More recent cars should be better.

The easiest way to check is to time the car on cruise control at some set
speed (e.g. 70mph) against the 100m marker posts at the side of the
motorway.

Even the degree of wear on  your tyres can affect the reading by up to 2%,
however if the reading is out by more than about 8% check that the right
wheels and tyres are fitted.  I looked at a 750i recently, lovely 19" alloy
wheels and 40 profile tyres - I rang a tyre dealer to check they weren't to
big, only to find they were actually too small!

Assuming you are allowing sufficient time at steady state speed for several
GPS data updates (12 seconds or so) and are locked onto 3 or more satellites
(usually you will be locked on 6 or more) the Garmin will be accurate to
less than 1 mph - probably less than .5 mph or better.  GPS is incredibly
accurate measuring speed.

RCE

I too have a Garmin, and as another poster has stated, they are very
accurate.

My '96 E36 reads almost exactly the same as yours. 3mph high at 30mph,
slowly rising to 5mph by about 60mph. At which point it stays 5mph
high all the way to 100mph (which is as far as I tested to).

As for testing them, in the UK you're tested every time you go past
the big yellow boxes on poles!

Dodgy.

I don't think the "error" is built in since it is inconsistent.  My X5
reads 1 MPH faster than the GPS at 60 mph.  My 3301 reads 3 MPH faster
at the same speed.

Since both are leases, I checked the car's odometer against the GPS.
They are both very close but do run a bit higher than they should.  Over
36 months/45K miles the difference isn't enough to cost me anything at
the end of the leases for extra mileage.  My guess is that, worst case,
the 330i will pick up 200 miles or so over that time.  I'm not that
close for it to matter.

FWIW a Pacifica I rented last week was dead on at 80 mph with the cruise
control set.

Dan

Yes, the GPS should be accurate to a greater degree than the car.

If the car reports 70, you actual speed should be in the range of 67, give
or take an mph. You are noticing a normal condition, but perhaps a bit on
the extreme edge of what should be normal.

You can test with a stopwatch and a measured mile. The freeways have
milemarkers on the side, and you can divide 3600 by the time it takes to go
a mile with the Cruise Control set, and see if the speed that results
matches the speed reported by the GPS or the speedometer.

This is normal. Seen it on every bmw. Your gps is accurate, the BMW is
not. 5 mph sounds about right with what I have seen. Same story on
Audi, I think they do it on purpose.