user2454: I see this all the time: a character is doing something on a computer or watching TV. Instead of filming the actual content of the screen, they film the scene with a fixed camera and add a layer with the content they want to show during post production.
Here is an example (from a TV series named Underemployed, Season 1 episode 1 at 18:42). 
In this case, you can see that the perpective correction is wrong (the bottom right corner doesn't match the actual corner of the screen), and I'm really wondering what I'm looking at. It looks like a deformed iPad application displayed on a cheap PC, I really don't know.
What kind of problems occur when you film an LCD ? Is it a technical issue, or is there another problem I'm not thinking of ? Maybe a logistic problem (like.. the actor doesn't know how to use a computer, or they should synchronize the actors play with the content played on the TV..).

user1890: The problem with recording a video display with a video camera weather LCD, LED, or old fashion CRT is the frame rate often does not match the camera. Artifacts may include a vertical bar rolling through the screen. Even if your camera can match the frame rate of the display being recorded one may still end up with moiré pattern artifacts.
Many productions find it easier to either cut out the display and add by compositing and masking another layer for the desired content. Another way is to green screen the display area and use chroma key to add the additional layer of content in post production. Not everyone is great at setting up the perspective correctly in post. One needs a professional video editing software that has the ability to alter the added layer with track motion that has x, y, z axis controls. This is not a trivial task.
Other possible solutions may involve the use of gen lock and frame lock systems.

user-1: There are several factors that comes to play with recording computer screens.

As filzilla already mentions, sync is a major factor. In the old days CRT monitors was very challenging to film even with sync-locking. Depending on if you filmed on silver or on video you did get different results. With the exception of LED screens, LCDs also offer sync problems.
The other factor is light conditions. For movie scene you usually have a large amount of light which a computer screen is unable to produce - so the screen turns very dark. You also get problems with color-correction/white-balance as the monitor typically have a different color temperature than the lights used to lit the scene.
The third factor is of more recent nature and has to do with the nature of LCD screen and it's polarization, referring to the limited angle they are visible within. You will get "gradient" effects and on more poor screens also have limited visibility from the sides, top and bottom.
Moiré can be a problem. For video this isn't such a big problem because the light coming from the screen will blend the pixels. Unless you have a high resolution camera filming in low(er) light conditions, or are filming close-up (but not so close that you can actually see the screen pixels), the camera won't be able to separate the individual pixels. For movie cameras this is more present though due the higher resolutions and the requirement to light conditions.
Then there is content synchronization with the actor's interactions or the scene in general, the potential of typos, wrong clicks, having to reset for each take and so forth.

It's more easy to put in a video in post which you can color correct and adjust, synchronize and so forth to the movie.
The process isn't very complicated. The computer screen is often recorded with a green or blue backdrop to eliminate the need for mask/matte rotoscoping. You just track the corners of the inner part of the screen and drop in a keyed replacement for the screen.
There are plugins too that do a pretty decent job automating this process (or instance the Mocha AE and its planar tracking).

2454: <p>I see this all the time: a character is doing something on a computer or watching TV. Instead of filming the actual content of the screen, they film the scene with a fixed camera and add a layer with the content they want to show during post production.</p>

<p>Here is an example (from a TV series named Underemployed, Season 1 episode 1 at 18:42). <img src="https://i.stack.imgur.com/hX76B.png" alt="screen changed at post production"></p>

<p>In this case, you can see that the perpective correction is wrong (the bottom right corner doesn't match the actual corner of the screen), and I'm really wondering what I'm looking at. It looks like a deformed iPad application displayed on a cheap PC, I really don't know.</p>

<p>What kind of problems occur when you film an LCD ? Is it a technical issue, or is there another problem I'm not thinking of ? Maybe a logistic problem (like.. the actor doesn't know how to use a computer, or they should synchronize the actors play with the content played on the TV..).</p>
 1890: <p>The problem with recording a video display with a video camera weather LCD, LED, or old fashion CRT is the frame rate often does not match the camera. Artifacts may include a vertical bar rolling through the screen. Even if your camera can match the frame rate of the display being recorded one may still end up with moiré pattern artifacts.</p>

<p>Many productions find it easier to either cut out the display and add by compositing and masking another layer for the desired content. Another way is to green screen the display area and use chroma key to add the additional layer of content in post production. Not everyone is great at setting up the perspective correctly in post. One needs a professional video editing software that has the ability to alter the added layer with track motion that has x, y, z axis controls. This is not a trivial task.</p>

<p>Other possible solutions may involve the use of gen lock and frame lock systems.</p>
 -1: <p>There are several factors that comes to play with recording computer screens.</p>

<ul>
<li><p>As filzilla already mentions, sync is a major factor. In the old days CRT monitors was very challenging to film even with sync-locking. Depending on if you filmed on silver or on video you did get different results. With the exception of LED screens, LCDs also offer sync problems.</p></li>
<li><p>The other factor is light conditions. For movie scene you usually have a large amount of light which a computer screen is unable to produce - so the screen turns very dark. You also get problems with color-correction/white-balance as the monitor typically have a different color temperature than the lights used to lit the scene.</p></li>
<li><p>The third factor is of more recent nature and has to do with the nature of LCD screen and it's polarization, referring to the limited angle they are visible within. You will get "gradient" effects and on more poor screens also have limited visibility from the sides, top and bottom.</p></li>
<li><p>Moiré can be a problem. For video this isn't such a big problem because the light coming from the screen will blend the pixels. Unless you have a high resolution camera filming in low(er) light conditions, or are filming close-up (but not so close that you can actually see the screen pixels), the camera won't be able to separate the individual pixels. For movie cameras this is more present though due the higher resolutions and the requirement to light conditions.</p></li>
<li><p>Then there is content synchronization with the actor's interactions or the scene in general, the potential of typos, wrong clicks, having to reset for each take and so forth.</p></li>
</ul>

<p>It's more easy to put in a video in post which you can color correct and adjust, synchronize and so forth to the movie.</p>

<p>The process isn't very complicated. The computer screen is often recorded with a green or blue backdrop to eliminate the need for mask/matte rotoscoping. You just track the corners of the inner part of the screen and drop in a keyed replacement for the screen.</p>

<p>There are plugins too that do a pretty decent job automating this process (or instance the Mocha AE and its planar tracking).</p>
