Thousand word paragraphs look bad no matter what medium they're displayed in. In a normally-printed paperback, a thousand word paragraph would be a page and a half long. 1000 words in ten point font take up a whole side of A4 paper. Imagine how bad a ten paragraph dissertation would look!
The main difference between a screen and a book is that a column in a book is four inches (and ~12 words) wide, while a column on a screen is 12 inches (and ~25 words) wide. This is a much larger distance for the eye to travel, and people who are not used to reading off a screen can have difficulty with it. To be really technical, when reading a book, most of the line is seen by the fovea at any given time, whereas when reading a screen less than a fifth of it is. Scanning back to the start of the line is much more difficult, as to the eye , most of the text is an indistinguishable blur.
There are easy workarounds though - most browsers allow you to select text, and show your selection in a different colour. This highlighted text gives the eye a reference point, distinguishable even though it is not in the fovea. The highlight need not even be on the current line; the eye can seek quite well to the start of lines within an inch or two of change in colour. It's only with large blocks of the same colour text that it has difficulties.
This is why normal paragraphs are easy to read on a screen; the eye can use the gaps between paragraphs as landmarks.
It has been suggested that long paragraphs on computer screens are difficult to read because of the flicker. This is incorrect, however, as the same paragraph is as difficult to read on a CRT screen (which does flicker) as on an LCD screen which does not.
It has also been suggested that LCD screens merely flicker less than CRT screens. This is also incorrect, as because of their completely different technology, LCD screens do not flicker at all.
Phosphor-based screens (CRTs, Plasma screens, CRT projection screens) flicker, because the image is produced by small dots of phosphor1, which produces light when it is excited by high-energy electrons. When the phosphor is not being excited, the light output steadily drops. Rather than excite each phosphor all the time (which would require an enormous amount of electronics), the phosphors are excited in sequence by a single electron source2. While the electron source works on other phosphors, the phosphor discharges its stored energy. Depending on the formulation of the phosphor this may take a long (providing a bright, low-resolution, high-contrast image that deals poorly with motion), or short time (providing a dim, high-resolution, low-contrast image that deals well with motion). Televisions, and text-mode monitors use the former, modern monitors use the latter. LCD screens behave completely differently.
An active matrix LCD screen is an array of subpixels, each of which produces no light itself. Each subpixel is made up of a tiny memory cell, a dot of liquid crystal, and a coloured filter (to make it red, green, or blue). The subpixels are illuminated from behind (usually by a cold cathode lamp), and (depending on the state of their memory cell) allow some, all, or none of the light through. Because the liquid crystal is constantly powered by its memory cell, it does not flicker, and does not need to be refreshed.
The 'refresh rate' of an AMLCD is the rate at which visual information is written to the memory cells of the active matrix: while the liquid crystal can stay at a constant transparency indefinitely, there is an upper limit to how fast it can change this transparency. More expensive screens can change colour, and therefore refresh, faster than cheap screens.
Older 'passive matrix' screens do flicker, because their liquid crystal cells are driven by capacitors, charged by pulses which scan across the screen. Aside from flickering, these obsolete screens had enormous problems displaying moving objects (such as the mouse pointer), and are virtually impossible to get hold of nowadays. Every computer, laptop, mobile phone, and handheld console3 produced in the last five years has an active matrix screen.
1 - Not phosphorus, though most phosphor formulations contain a lot of phosphorus.
2 - To be really pedantic, plasma screens have one electron source per phosphor, but these are powered by a much smaller number of energy sources, which scan across the screen in much the same way as a CRT's electron beam, or a passive matrix's transistor pulse.
3 - Compare the horrible blurry gameboy and gamegear with the newer active-matrix gameboy colour and gameboy advance
'LCD monitors - Of Pixels and Pitches' : http://www.computerwriter.com/archives/1998/cw092498.htm
'Thin-film Transistor LCD Displays' : http://www.cs.ndsu.nodak.edu/~revie/amlcd/