When we just join the meshes, we simply throw them all, unnaltered into the same bucket. Then we can jump into edit mode, select a single vertice/edge/face and press ctrl-L (THIS is a timesaver) to select Linked ones. If we have a vertice on one flower petal selected, all vertices that are connected by edges to that vertice will be selected, as will all connected from those, ect, until the whole maze of interconnected vertices is selected and we wind up with all vertices making up that whole, single petal selected. If any vertices between this petal and another one had been merged, you'd have all vertices of both petals selected. This will also affect normals - that is which way the vertices are facing (however silly a concept that sounds for a unsizeable point), resulting in a smooth transition between the petals, when shaded, whereas if they are kept separate, each petal will be shaded according to their own respective curvature. Damn, I formulated that badly, but I'm late for work already...

Union, Intersect and Difference corresponds to OR AND and AND-NOT, respectively.
Union (OR) will produce a result from the *volume* occupied by ANY of the two objects, so if we have two cubes intersecting, it will still look like two cubes intersecting. However, we are only keeping keeping the outer hull of the conjoined cubes - if you look inside it, you'll notice that there is free passage between the cubes. If we had JOIN:ed the cubes, rather than OR:er them, we would simply have kept them as they were and you'd have had their walls making up a smaller box inside them.
Actually, if there is no need to go near the interecting area, in-game, simply joining means you have fewer vertices and faces and shading becomes correct (as explained above), whereas union will create a new vertex wherever edge meets surface.
Intersect (AND) will produce a result from the *volumes* occupied by BOTH objects, so if we have have two cubes intersecting, we will get a smaller box, made from the overlapping parts. Really the bit that was removed in the union operation.
Difference (AND NOT) will produce a result from the *volumes* occupied by one object, but not he other, in effect letting the latter take a bite out of the former. It is really AND, with the cutting_tool cube warped inside out, like that nice resting home for the mentally deranged in So long and thanks for all the fish, so that it is everywhere, except in the small space enclosed by its outer walls... :7
@pappou:
If you are actually making that building for use, rather than practice, I'd suggest building the parts separately:
- Make a pillar from a box, removing the end caps, which we'll never see anyway. This pillar can then be duplicated several times, to make the other ones, with subtle texture alterations to make them not too identical.
- If one can not enter the building, walls can be planes, rather than hexahedrons. Stageworks takes less wood than real houses..

- Just map that nice occluding woodwork onto a plane and then start a new object -- you can begin with a circle or something, if you like and then start moving its vertices, to trace the outline. Delete any left over vertices, then select them all and extrude perpendicularly. Then extrude again, to add the front and back faces. At the upper edge, you can probably just keep the two corners vertices and merge all the ones in between to either of them. Now just make sure the normals are facing outwards.

This building element too, can simply be copied to the other openings (or used as a boolean cutting tool, should you want to). Actually (and now I'm getting even further out of scope) , if there is no need to view it up-close, I'd just keep it a simple plane and map the texture onto it, with any holes alpha-painted transparent in, you were using Photoshop, I think?It will be paper(or rather infinitly)-thin and subject to image resolution, but very easy on the GPU.
@Junee:
You could breifly try to reduce the graphics acceleration settings for Vista and see whether that helps with your Blender graphics glitches. I believe there was talk in another thread, about the storage of user files in different versions of Windows -- me, I just keep all my blend files in the .blender directory.