Using this technical explanation of the Holodeck's emitter field function, it makes sense that an image, a visual construct might be able to be seen leaving the holodeck the same way a ray of light might be seen leaving a room. But as soon as the construct leaves the holosuite room, they are likely only a light construct or feeble field construct that will fade as:
- either the holodeck doors close, blocking the field emissions into the hall.
- or they walk out of the range of the field that creates the three-dimensional-appearing matrix of the character leaving the room.
The technical specifications for the emission technology used in the holodeck should allow a visual construct to exist as long as they are in the doorway of the opened holodeck door. Remember, images create are a mixture of light, forcefields and replicated matter as necessary. This mixture may not be noticed by the user of the room and might give the illusion of a character being able to "walk" out the door, but not much further.
As far as other flubs of the holodeck consider them to have been applications of replicated matter (water on Wesley, or lipstick on Jean-Luc for example) which might continue to exist once a user of the holodeck leaves the area. A snowball might also be able to leave the holodeck if it were actually comprised of replicated matter rather than an animated force field. (though if the person were standing in the doorway, they may be able to be struck since they they would be within the field generation window.)
Active safety protocols of the holodeck may prevent more lethal projectiles or forces from leaving the room or passing under the arch as a protective feature.
From the Wikipedia entry on the holodeck technology.
The basic mechanism behind the holodeck is the omnidirectional holo-diode (HDO or OHD, its acronym in English). The HDO comprises two types of micro-miniature devices that project a variety of special force field. The density of HDOS in a holographic surface is 400 per square centimeter, fed by an outlet electroplasma medium power. Entire walls are covered with HDOS, manufactured in an inexpensive process of printing circuits on a roll.
A typical surface holodeck includes twelve sub-layers processed a total of 3.5 mm, fused to a thermal-structural light panel, which on average is 3.04 cm thick. The primary materials include sub-processor/emitter of superconducting material. Each individual HDO measures 0.01 mm. The mechanism of digital optical network, by which an HDOS receive impulses, is similar to that which feeds smaller display panels, although the walls are divided into major sections, and easier to control with greater speed, each with 0.61 m². Sub-sections which are dedicated to the main computer can control such "monitors" which are the size of rooms.
Besides the ability to project stereoscopic color images, HDOS manipulate the force fields in three dimensions to allow visitors to "feel" objects that are not really there. This tactile stimulus provides the appropriate response one would expect from a rock on the ground or a tree growing in a forest. The only factors limiting the number and types of object are given by the computer memory and time to retrieve or calculate the beginning pattern of an object, either real or imaginary.
The version of "optics" of a HDO sends a complete picture of the environment or landscape, based on their location relative to the full panel. The visitor, however, sees only a small portion of each HDOS, almost like a fly's eye operating in reverse. When the visitor moves the visible portions of HDOS change, changing the perspective. In reality, the energy emitted is not a visible electromagnetic emission, but is actually polarized patterns of interference. The image is reconstructed where the patterns intersect the lens of the eye or any visual receiver.