An object approximately the same size as Pluto, Eris, was discovered only 8 years ago (in 2005). Are there any Pluto-sized objects remaining to be discovered, and if so, how far away from the Sun would they have to be to not have been detected already?
This is a part answer to your question, as it is difficult to answer without speculating, so here are some facts/observations related to your question.
Asides from Pluto/Charon, Eris, Triton (could be a captured Kuiper Belt object), Makemake and the football shaped Haumea, most of the Kuiper Belt Objects (KBOs) are according to the article "Kuiper Belt Objects: Facts about the Kuiper Belt & KBOs" (Redd, 2012):
thousands of bodies more than 62 miles (100 km) in diameter travel around the sun within this belt, along with trillions of smaller objects, many of which are short-period comets
and is believed to have a total mass of only a tenth of the Earth, according to the article "Forming the Kuiper Belt by the Outward Transport of Objects During Neptune's Migration" (Levison and Morbidelli).
Here is a list Of the many Transneptunian Objects that have been documented, detailing their absolute magnitudes.
In regards to one of your main questions - according to Redd (2012), the challenge in their detection is
Because of their small size and distant location, Kuiper Belt Objects are a challenge to spot from Earth. Infrared measurements from NASA's space-based telescope, Spitzer, have helped to nail down sizes for the largest objects.
I would add, their irregular elliptical orbits* and extreme (compared to the major planets) inclination to ecliptic make it that much more difficult to detect them. Additionally, according to "The Edge of the Solar System" website, further difficulties include low surface reflectivity.
- An example of a possible KBO with an extremely elliptical orbit is Sedna, which is believed to take over 10,000 years to orbit the sun; is smaller than Pluto, but was observed at about 90AU (3 times further than Pluto).
So, there could be many small Pluto-sized 'dark' worlds in highly elliptical irregular orbits in the Kuiper Belt and beyond. However, beyond those listed, we have not seen that many and the total mass theorised does not support the idea of too many in existence, but that does not mean that they are not out there.