There are a couple of things going against Sony E 16/2.8 in the resolution department - firstly, it's a moderately fast ultra wide angle lens, and secondly it is a pancake lens. Very rare 15/16mm UWA lens would perform equally well across the entire frame and all apertures. Not only such lenses are rare, they are also extremely expensive. For example, Contax 15/3.5, which is actually almost a full f-stop slower, costs ~$2,600. Nikon's 15/3.5 Ai, goes for ~$1,000. We will be kidding ourselves if we think that the $250 Sony 16/2.8 would perform on the level of higher end UWAs. And on top of that, pancake design limits designers to more simplistic optical formulas - Sony's E 16/2.8 is a 5/5 design, while Contax 15/3.5 is a 13/12 design, so yea, a lot of stuff will not get corrected to the same extent (BTW, I'm not arguing that a complex optical formula it always the best solution - look at the Cooke Triplet and it's modern variants to get an idea of how good simple designs can be). Anyhow, there is one advantage that E 16/2.8 has though - it is an APS-C lens, so it has to benefit slightly from a smaller sensor coverage. In theory...
Taking the above said into perspective, we can argue that Sony E 16/3.5 performed as one would expect it to perform. Per Imatest chart below, the lens shows a fairly noticeably softness around borders at wide apertures. This is expected, but APS-C size sensor did not really help much here, which is a bummer. The lens is fairly soft around corners through f/5.6. Smaller apertures beyond f/5.6 look more acceptable, although results don't seem to be tack sharp here either. On the positive side though, image center should be very sharp according to this chart - it remains fairly sharp throughout the tested aperture range, although resolution seems to degrade slightly beyond f/5.6.
There are no real surprises when we look at the imaging target crops - corners at f/2.8 are noticeably soft, and there is not much that can be done. Even f/8 is not really sharp as with some of the higher class lenses. But not much we can do here, so let's move on to the field test before wrapping up with this section.
The field test, which was done at the focusing distance of ~10m, does not really reveal anything new. Image center remains pretty sharp straight from f/2.8, but borders at wider apertures are still soft. They do seem a little bit better than in the imaging target crops, but maybe it's just my imagination. You would need to stop the lens down to f/5.6 or even f/8 to get borders reasonably sharp. Notice that there's some distortion around extreme corners, which also degrades the overall feel of sharpness. If you are finicky about your corners, say you're an architecture or landscape photographer, you should use this lens stopped down, which unfortunately might be suboptimal.
Color & Rendering
The color reproduction capabilities of this lens are very similar to most other, consumer-oriented, Sony NEX lenses like the kit 18-55/3.5-4.5 kens. You get moderate levels of contrast throughout the aperture and a reasonably well balanced and neutrali-ish color gamut. With about average tonality across the aperture range, you also should not expect any negative (or positive) surprises in how this lens renders subjects, (some might even call it boring). Because the lens vignettes a little bit at wider apertures, you might want to consider upping EV compensation by ~0.5EV.
Unfortunately, the lens also shows rather high levels of lateral CA around borders. From Imatest's chart below, CA reaches ~2.1px at f/2.8. In practice, you would see some CA around image borders at higher magnification. This is more pronounced in high contrast images, for example around brightly lit neon signs in a dark bar (see the picture in the sample gallery).
DOF & Bokeh
The bokeh characteristics of Sony E 16/2.8 can be summarized in one word - mediocre. It is hard to expect anything spectacular from a 16mm UWA lens, so this should not come to you as a surprise (I hope). The highlights are uniformly lit, and seem neutral to the eye. There are no major signs of longitudinal CA in OOF areas and there does not seem to be any major change in contrast when shooting the lens at close focusing distances. So why say that bokeh is mediocre? There is not much bokeh present, since the lens retains quite a lot of detail in the background no matter what aperture you use, and the feel of separation is practically non-existent - the only lens that is worse in this department is a 14/2.8 prime (well, maybe also a fisheye lens) . Yea, there's not much to talk about here, so let's just move on...