What are the current observational limits on the existence of Dyson spheres/swarms/rings? A Dyson sphere/swarm/ring is a hypothetical structure an extra-terrestrial entity would construct to collect a large fraction of its host star's light, and would likely generate a fairly strong infrared signature that could potentially be detected by modern infrared surveys (such as WISE). Do we have any meaningful constraints on the existence of these structures within the Milky Way (or beyond) from these surveys? What sorts of natural phenomena could be confused with such structures, if they existed?
Reading Dyson's original argument gives some useful information. He says that such a sphere would have a surface temperature of 200-300 Kelvin, as it would reradiate some of the energy it absorbs at infrared wavelengths. That's a temperature comparable to cool Y-type brown dwarfs. If we can assume a black body approximation, and a radius of about 1 AU, we get a luminosity for a 200 K sphere of
$$L_{\text{DS}}\simeq4\pi\sigma R^2T^4\sim10^{25}\text{ Watts}\simeq0.1L_{\odot}$$
That's substantially more luminous than a cool brown dwarf of the same temperature. Additionally, Planck's law gives a peak black body wavelength of about 14,500 nm, placing the emissions in the mid-infrared range, as expected. Relatively hot brown dwarfs should be expected to have high infrared emissions. In other words, a Dyson sphere should look something like, from a distance, a large, luminous brown dwarf.

Dyson spheres, in the classic picture of a solid shell enveloping a star, are actually unstable, so it's unlikely that they would ever be built. We should expect other variants - Dyson swarms, rings, bubbles, etc. - that are composed of large arrays of smaller objects are much more likely to be created.

Fermilab used data from the Infrared Astronomical Satellite (IRAS) to look for Dyson spheres as a secondary mission, searching a band in infrared wavelengths centered around 300 K (see Carrigan (2009)), covering 100 K to 600 K. The study started with 250,000 sources over 96% of the sky, then whittled them down to about 6,000 based on temperature range and flux. 17 "ambiguous" candidates were finally left. This is, to my knowledge, the most complete survey yet undertaken.

There have, of course, been others, most using IRAS data. WISE and 2MASS also contributed data. Very few candidates have been found, and it has been estimated that any within about 1 kpc in reasonable temperature ranges (less than 400 K) should have been among these.

There are indeed natural sources that could prove to be false positives. Carrigan lists several:


Dust shells around stars possibly undergoing mass loss
Stars embedded in dusty areas, including dense nebulae
Mira variables, which undergo mass loss towards the end of their lives
Planetary nebulae
AGB stars, which may create circumstellar envelopes, as well as post-AGB stars