Can the difference between a star and a galaxy which are point sources be detected?
Obviously a star would be a point source. A galaxy should be an irregular blob if close, but if it is far away then it would seem that a galaxy too would be just a point source.
Given that the star and galaxy were both only detectable as point sources can astronomers tell them apart with redshift? By some other method?
A followup question...
What percentage of galaxies if our universe can we only detect as point sources?
To distinguish galaxies from stars, you can use the spectrum. Roughly, stars have a black-body like spectrum with features depending on the absorption and emission on the line of sight and in the chromosphere of the star.
Galaxies on the other hand of a spectrum that is the composite of tons of stars. The spectrum will for example be much wider (ranging from smaller to larger wavelengths) because of the diversity in the spectra of stars.
Take a look at http://www.atnf.csiro.au/outreach/education/senior/astrophysics/spectra_astro_types.html if you want a quick overview of the differences.
I don't have a precise number about the number of galaxies we see as point source, but the answer varies greatly from one instrument to another one. If you try to observe a galaxy using radiotelescopes in interferometry, you can resolve much better scales than an Earth-based small visible telescope, etc…
Has it been possible to actually reach that high resolution to detect different bands from the highly redshifted spectrum?
Also, the stars in a galaxy have more motion than the surface of a star, the lines will be more blurred out by doppler shifting.
You can also poke around in images produced by the Sloan Digital Sky Survey (SDSS) that have a resolution of about 1 arcsec and compare them with images from the WISE Atlas, that has a resolution of about 10 arcsec (6 arcsec native, convolved with the PSF to improve sensitivity of detecting point-like objects). Compare the galaxy at (179.710668548, -0.438511083) - nice and resolved in SDSS, featureless dot in AllWISE.