It doesn't look all that bad to me! It's been a horrible summer just about everywhere and the plants are showing it; it's also about the end of the growing season, and the plants are showing that, too. Here's what I got from your pictures:

1:don't know
2:probably hydrangea, need closer picture
3:ditto
4:ditto
5:Lavender
6:Lavender
7:don't know
8:don't know
9:Hydrangea
10:Hydrangea
11:Rose, I think, but need closer picture
12:If same plant as 11, same answer
13:Rose of Sharon
14:Rose of Sharon
15:don't know
16:don't know
17:probably hydrangea, need closer picture
18:ditto
19:don't know
20:don't know
21:Peony, I think; if same plant as 22, yes, Peony
22:Peony
23:probably clematis, need closer picture
24:if same plant as 23, ditto
25:don't know

You might want to check with your landlord as to what is expected - it may be just that the lawn is mowed weekly and the weeds don't take over.

This was a particularly bad year for hydrangeas around here (north central NJ), so yours don't look all that bad to me; they just get ratty at the end of the summer.

I recommend that you ask for help with your IDs in the Name That Plant forum here at Gardenweb, as you are more likely to get a quick response than you are here - just saying.

Excellent, thank you so much! This will get me a fantastic start in just where to do my research. And I had not noticed the Name That Plant forum, the New to Gardening caught my eye first and it seemed appropriate.

Thanks so much again!

To tidy up: you can leave the Hydrangeas until spring. They will gleefully drop all their leaves for winter and keep their dry flower heads. They can be cut to the ground once midwinter has passed and they will put up new stems. Or you can cut back what's there at various heights just above a pair of fat buds (they're the leaf-growers) in late winter or early spring so you still have a visible bush. Ask a neighbour what the local custom is.

Get yourself some decent secateurs, by-pass style for preference, and loppers perhaps. Cheap ones often break, can be hard to sharpen. Keep them sharp. You'll be so glad you did.

Lavender - and it looks like english lavender - is actually quite easy to maintain. Use sharp hedge shears and trim them all over to make a ball shape. When you look at a stem you'll see brown wood and green wood. Make sure, when you're trimming, to stay in the green wood zone.

If you're feeling nostalgic, you can save the dry heads for hanging in the wardrobe to scare away the moths. The heads hold their scent for ages.

I'm guessing you're either zone 8b or zone 9 because the plant with the glossy leaves looks like a Camellia. At this point it doesn't need 'tidying' or pruning. It's only a youngster. Flowers in spring and it helps if you clear away the fallen flowers in spring (they make a heck of a mess), plus giving them about an inch of mulch once the ground warms up so they don't suffer from dryness.

The Clematis has escaped to the top of the trellis. They do that. Which is fine if you're over six feet but disappointing otherwise. There are several different sorts of Clematis. Ask your landlord what was planted before you prune it back. If it's a jackmanii - you can cut them off at about four feet so the new spring shoots start from lower and you get the flowers starting lower down.

That rose. Oh. Somehow contact your local garden club or garden centre and ask if there is a person they'd recommend for rose pruning. That one looks like a climber with ambition. It would be better thinned out and given persuasion to flower closer to the eyes of the beholders. Get help for this - and either dispose of the clippings in your incinerator, if you have one, or take them to the local green waste disposal point. (Make sure all the trimmings are off the garden. Clutching dry rose stems while weeding is, um, painful...)

I'm not sure of the grasses. However - please note the mulching around them and replace ASAP - before the weed seeds blow in. And take off their seed heads, too. To save yourself unnecessary weeding work.

If you have someone in your area who does lawn-mowing at an affordable rate - hire them, if the budget will stand it. And make sure they do the edges. Trim edges make the place look tidy 'instantly' - even if there are little weeds in the beds.

The little plant with the oval blue flowers is a Viola/pansy. It may or may not be perennial for you. They get leggy after a while, and spit seeds around - which is not bad - and die out. It's up to you whether you replace it.

Save yourself excess work by never letting a weed go to seed and keeping the mulch cover intact - whether it is bark chips or well-seasoned compost. Both will reduce the need for watering, though you will have to water at least once a week and thoroughly. If you property comes with a drip-watering irrigation system on a timer - use it to save yourself from tedium, insect bites and lost time from playing with the baby.

And, with care, you could ask among the 70 year old retirees for assistance/information on how to save yourself unnecessary work in the yard.

I would think, if upkeep is mandatory, that your landlord should provide a guide! I'm sorry that you had to take time to learn about the plants, but happy you did. I just think the landlord has a responsibility here.