When riding minecarts, with my friends on our server,
we can no longer see eachother when one leaves his/her minecart.
The players turns invisible for one another until one logs out and in again.
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This also happens on my LAN server. Though the player turns visible after a few minutes.
Also after entering/exiting (can't remember) a cart sometimes the player displays at distanced places and walks through walls for a few seconds. I'll try to get that as video.
Me and a couple friends experience this frequently on a server hosted by a friend off his computer. As soon as the player riding a cart moves out of your loaded chunks range, what is it 15x15 chunks, his model will often remain at that location. If you ride a cart up after him you'll see his model hovering in air without flapping there only to disappear after a little while or as you approach. But when arriving both players will usually not see each other until after a while or a relog.
I can confirm what Mikael Hartwig-Karlsson wrote. Very annoying.
Is this still a concern in the current Minecraft version? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.
Still in 1.4.6. At high altitude I was able to observe the behaviour on short tracks. There I even got one minecart driving UNDER the track.
By the way: die player avatar is still sitting at the place where he started the ride (On long tracks the avatar mainly stuck somewhere standing along the track).
It exists in the snapshots too, last one i checked was 13w05b.
This was on Windows 7 aswell so it's not limited to Linux.
Players appear to be jumping around because the game uses the same packet to mount and unmount entities.
Ive made some changes that appear to fix the floating players. I haven't experienced any players becoming invisible though.
In EntityPlayer add the following method:
EntityPlayer.java
public void mountEntitySpecial(Entity par1Entity) {
if (this.ridingEntity != par1Entity) {
super.mountEntity(par1Entity);
}
}
In NetClientHandler change the handleAttachEntity method:
NetClientHandler.java (Before)
if (riderEntity != null) {
((Entity)riderEntity).mountEntity(riddenEntity);
}
NetClientHandler.java (After)
if (riderEntity != null) {
if (riderEntity instanceof EntityPlayer) {
((EntityPlayer)riderEntity).mountEntitySpecial(riddenEntity);
} else {
((Entity)riderEntity).mountEntity(riddenEntity);
}
}

Ugh. That's kind of a kludge to get around the kludgy code that's already there. I tried to simplify that mess and ended up about where you did. Except it shouldn't be necessary with the changes to mounting in 1.6.1, or more specifically, the changes to unmounting. Since you no longer dismount by right-clicking the mount, but instead push the sneak key, EntityPlayer should no longer need to override mountEntity, and the check for "this.ridingEntity != par1Entity" should go right in NetClientHandler.HandleAttachEntity.
I see what you mean. I completely forgot they changed it. After testing in 1.6.1 the bug does appear to be fixed.
It is still a concern in the 1.8.1-prereleases, both with boats and horses... not sure about minecarts tho'.

Reopened, thanks

Can't confirm in 1.10.
Even when driving from a location far away of other players (not streamed in) a single cart will drive and it will take time for the player to display.