How to get the rest of the catalog items back

The Animal Crossing: New Leaf catalog is accessable from a machine within T&T Mart and later upgrades to that store, and includes:

• Furniture
• Wallpaper
• Flooring
• Shirts
• Pants
• Dresses
• Hats
• Glasses
• Shoes/Socks
• Umbrellas/Parasols
• Stationary
• Music
• Gyroids*
• Fossils*

That said, all items that are available in the catalog are not necessarily available for order. In some cases, this is true for entire classes of objects -- marked with a * above. Some rare furniture (such as furniture you earn as an achievement or receive through a special event) cannot be ordered. I will not list them all here, but some general guidelines:

• Nintendo items cannot be ordered
• Special Event items cannot be ordered
• "Achievement" items cannot be ordered
• Items dropped from balloons cannot be ordered
• Items obtained from the island cannot be ordered
• Certain DLC sets, like the 7-11 series, cannot be ordered. There are some exceptions to this. I'll keep a running list here and edit it as I find out more.

The following DLC sets can be ordered from the catalog:

• American Best Buy DLC. So far, the Raccoon Wall Clock is available for order from the catalog for 1,920 bells. We can probably assume that the remaining Best Buy DLC will also be orderable, but we will need to wait to confirm that as they are only released every 2 weeks.
• American Spotpass Content
• Japanese "Campus" Set

As to your second question -- yes, all you have to do to get an item in your catalog is to hold it. "Holding" is fairly popular in online AC trading right now. I've seen players trade fairly valuable items for the opportunity to "hold" entire furniture sets, or Japanese DLC items. Players do this so that they can fill out and complete their catalog.

Here's the gist of it:

• Don't run. The island is so small there's really no need, and if you're running, certain sensitive (and expensive) beetle types may flee before you can even see them on screen.
• Approach slowly by holding down A. This will slow you down and prep your net so you just release the button to swing. Some bugs can't even be approached without slowing down, and beetles in particular are jumpy, so play it safe.
• When the beetle stops moving, stop moving. The beetles have a little "dance" animation they do while they idle on the trees, unlike other tree bugs. If the beetle sits perfectly still for more than a couple frames of animation, it has been alerted to your presence. If you continue moving, the beetle will eventually fly away. Take deliberate steps with pauses every couple steps, and stop immediately if the beetle seems to pause. Wait for movement before taking another step or two.
• Different beetles have different sensitivities. Horned Dynastids you can practically walk right up to and touch before they'll run. Horned Elephant Beetles will run extremely quickly unless you time your steps well, guided by the above advice. You will learn the beetle's sensitivities over time.
• Chase away the fruit beetles (green little bugs) they're worth nothing. Don't even bother, except to fetch a single one for the museum/encyclopedia.
• The sound of a net hitting something will scare the beetles off. Refrain from catching other, cheaper bugs if near a beetle, that way you won't scare off the more expensive prize.