I wrote this kind of quickly, so I'm not going to bother with too much of an introduction. I've read at least one other suggestion that had a few good things (I believe webbed, hanging corpses was one of them), but here I'll just be listing some of my ideas for improving spiders.
(This applies to both Mirkwood and Mordor spiders.)
Spiders are pretty good as they currently are in terms of look and abilities, so I'll just be suggesting some new stuff. Spiders would be repelled by bright blocks, like Edhelmir, Durnaur, etc. But they'd be attracted to smaller sources (torches, fires, etc.). When a spider gets close to one of these, they'd break (eat) the light source. Obviously, torches within protected territory would be safe from this - the torches in spider pits wouldn't be, so those would have to be removed. Every once in a while, they should place down normal webs that will despawn after a while.
The ability to breed evil mounts has been needed for a while. The Wargs especially could use this, but this suggestion focuses on the creepy-crawlies.
When a grown spider is fed Man-flesh, or when they kill something, they'd be able to breed. This wouldn't require other spiders in the area, just the one - plus any web (not including the temporary placed ones). The spider would move near the web, and place a new item on the side of the block called a Web Sack. Just look at a spider's egg sack in real life if you want to know what it should look like.
Eventually, the sack would break, spawning 1-4 Spiderlings. Baby spiders resemble very, very small spiders, with dull eyes and stubby legs. These would have very low health, being able to be killed in a single hit. After a while, these would grow into full adult spiders. In the case of Mirkwood spiders, all these spider-children would grow into the normal black variant. You can right click the Web Sack with gulduril to breed the green variant, and with a bone to get the blue. Spiderlings wouldn't be able to attack or deal poison/slowness until they reach adulthood.
This special variant only spawns in nests in the Mordor Mountains. These are incredibly large and strong, with a light venom in their bite. As for their appearance, they'd lack the red eye on their back, their eyes would be darker and more numerous, and their flesh black. Also, they'd have horns. The Gloom-weavers will attack anyone with under +200 Mordor alignment. Be very careful, for these great spiders have 45 health points, and can deal 6 points of damage to unarmoured players, plus their poisonous bite. Luckily for good players, these cannot be ridden.
These nests spawn throughout the Mordor mountains and Mirkwood, especially Dol Guldur. Choked thick with webs and hanging strings, these dens are littered with skulls and waste blocks. Very dangerous places, not least because of the Gloom-weaver that may be waiting inside. Dens in Mirkwood would be large, shallow pits between trees, while those in Mordor would be large caves. Both are full of Spiderlings and grown Spiders, and Gloom-weavers may spawn in the Mordor variants.
Webs - Walking into a web (and a web of Ungoliant) will attract any nearby spiders. Spiders will place webs every once in a while, though they don't last long. Web of Ungoliant - Gloom-weavers temporarily place these in place of normal webs. If possible, they'll also now produce a darkness effect, lowering the light level around them.
Web Sack - Placed by breeding spiders. Has no function other than spawning Spiderlings after a while. Won't yield an item if broken.
Web String - These hang from the ceiling like Orc Chains, and have a lesser slowing effect to webs. Crafted two string above a slimeball on a Mordor or Dol Guldur crafting table produces four web strings. They can also be combined with bottles of poison to induce a very light poison effect on whoever walks through them. Spiders can also climb up these.
The Most Important Part of the Suggestion
Mordor Spider Pits should use the Nan Ungol banner instead of the regular Mordor one.