In terms of the studies (google for them, there are a bunch) the reasoning behind this article are as follows....

Obese women tend to have longer labours. That does NOT mean they are "complicated", that means that in a hospital an Ob who is twitchy to get to golf/bed/the bar will regard a normal labour for an obese woman to be a protracted one by HIS standards and then augment, CAUSING complications. The reasons for longer labours are twofold. The first reason is that having a lot of excess bodyfat tends to interfere with calcium levels in cells, and your uterine muscles (in fact all muscles) NEED calcium to contract in a strong and organised way. That doesn't mean you can't labour perfectly well, it just means you might take a while to efface and dilate, and in and of itself that is not a problem at all. The second reason is that while the cervix is dilating and the baby descending everything in the pelvis needs to get out of the way. SOME obese women have a lot of fat around their organs (although they are far less likely to than obese men) and this fat also needs to move out of the way to let the baby out. This can mean the late first, transition and early 2nd stage is a little longer for obese women too. Again, not a problem so long as mum is well-supported and allowed to rest properly between contractions.

The reason epidurals can be harder to site in obese people (obese men having spinal pain relief for injury or surgery present the same challenge) is because THE NEEDLES AREN'T LONG ENOUGH! The epidural needle is about 4inches long and has a stop on it - they insert it into the epidural space and then place the stop against the skin to stop it going deeper. If your epidural space is more than 3 inches from your skin the needle can be too short. MOST major hospitals should have needles long enough as that is hardly bloody rocket science!

I have obese friends and was about 101kg at delivery (though 181cm so not quite obese) and i have read an awful lot on this. In my view i would suggest the following for obese women:

1) During pregnancy stay active and eat well - fat around the vital organs and in the pelvic cavity is MUCH less common in physically fit individuals, and exercise is the key to keeping your bodyfat under your skin and not around your guts.
2) Have a doula or a good midwife as constant support - you might have a long labour, but your body is EVERY BIT as capable of birthing your babies as any other woman - it can be hard to remember that after several days of tiring contractions, so make sure you have really top notch emotional and practical support for your WHOLE labour experience (oftentimes you will be sent home from hospital until you're dilating and if you arrive at 4cm after 58 hours of labour it might be too LATE for the support of your ob or hospital midwife to make a difference, those early hours are valuable working time for your cervix and baby, and good support then will be invaluable - i do not subscribe to labour only being "real" when dilation hits a 4 - labour is labour as soon as you're having to work to meet the contractions, and you need support from then on).
2) Take calcium supplements during pregnancy and birth - 1000mg/day during the last month and 1000mg every 3-4 hours during labour is what my german midwife friend prescribes for her larger mamas. This will also help minimise your pain as the better tone you have and the more organised your uterus is the less "work" there will be for you to do - it will flow like a well-oiled machine.
3) Avoid spinal anaesthesia. I know this is flying in the face of him up above with the article, but really as someone else pointed out, if your labour will be long anyway, WHY would you counteract gravity and sacrifice the tone of your pelvic muscles? Obese women, like ALL women, should stay upright during contractions, ESPECIALLY once dilation is happening.
4) USE YOUR RESTS - between contractions rest as much as possible. Stay upright but resist the urge to march about trying to speed things up - a little walk every few hours is fine, but climbing up and down the stairs between every contraction for 10 hours will just exhaust you. Eat and drink for as long as you feel interested, your body will appreciate it as will your baby. An active labour needn't be an exhausting one and the more relaxed you can stay the more your body can use its energy to labour.
5) Use gravity during the 2nd stage. The birth stool, supported squats, hands and knees and so on are your friends! With bigger mamas especially lying on your back can really shut the pelvis, making it much harder work for you and babe to get to birthing. So stay upright, and have a doula, DH, DP, Midwife, bar or rope to hang from while you push.
6) Remember this bit of good news; one study i read suggested that positional problems in undrugged obese women with protracted labours are REALLY rare - your baby is very unlikely to "get stuck" due to a positional problem during labour because all that prelabour means s/he has a lot of time to get tucked up into a little ball of birthable joy.

Bx