Enormous, about 80% of the speed of light. Yes, this is an obvious problem. However ...

The answer to the last question is simple. The redshift-distance relationship for galaxies is not a theory, it is an observed fact. Therefore, Arp's hypothesis is absurd, on the grounds that it claims the falsity of known facts. It's not all about velocity, and we know it. Just do what I always suggest, and go back to fundamentals. Consider something so obvious that nobody has objected yet that I know of: Things that are farther away look smaller (the angular size distance), dimmer (the luminosity distance) & smoother (the surface brightness fluctuations distance). These are all obvious, primary indicators of distance. Galaxies of the same morphological type, as in the Hubble sequence, which are sytematically smaller, dimmer, & smoother, are farther away. Hubble saw that galactic redshifts correlate with these primary distance indicators, and that's how he came up with a redshift-distance relationship in 1929.

The correlation between redshift and primary distance indicators clearly means that high redshift galaxies are farther away than lower redshift galaxies. And since most cosmological quasars are clearly attached to galaxies of the same or similar redshift (example HST images), then they too are at the same distance as the galaxies that host them.

Now, years ago, Arp discovered what he though were improbable correlations between the locations of galaxies and quasars on the sky. But he calculated his probabilities wrong, and after a few years of discussion in the journals, his ideas were properly rejected. The obvious correct solution to the problem is not to do what Arp did, and deny the redshift-distance relationship, but rather to realize that were are dealing with different populations of objects.

So, there are distant, cosmological quasars, and there are nearby, non-cosmological microquasars. They are basically the same kind of thing, powered by a compact central engine (probably a black hole), but on different scales of size & distance.

Now, no theory is problem free, and standard theory & cosmology are no exception. I assume that the authors know how to determine a redshift properly, in which case we are presented with a bizarre problem. But, while a velocity 80% of light is a problem, it's not an impossibility. The Arp hypothesis that quasars are all local objects is an impossibility, and I prefer to accept bizarre over impossible.

Antoniseb asked if it might not be a quasar at large distance, virewed through the galaxy. I tend to doubt that, simply because the object which I call a microquasar may be too close to the center of the galaxy, where the bulge would make it hard to see through. But it is possible, and may be the simplest explanation, despite the difficulty. Look at the HST images of NGC 7319. Download the biggest screen image you can, I used the 3.2 Mbyte jpg image. As you can see, the extended halo of the galaxy is almost transparent, and background spiral galaxies are clearly visible through it. But I don't know the angular scale, and can't tell from the image published in Galianni, et al., where the quasar object is in this image. That would tell me whether or not I think it likely to be visible through NGC 7319.

That's all I can say for now.