Elderly mother visiting UK for first time - questions re visitor visa?

My elderly mother (70s) is planning on visiting us (and her grandchildren that she's not yet met) for the first and most likely only time. She will be travelling alone - my sister in the states is getting her to the airport at Dulles and we will be meeting her at the airport in London.

She will most likely be staying 3-4 weeks. Does she actually need a visitor visa for this? She obviously has no intention of staying longer and has family and friends and a home to return to, has money to support herself while she is here. She's mainly just coming to see us and to do a little sightseeing as she's never been to the UK before.

I'm just worried that the actual paperwork involved in a visa as well as gathering proof that she will be returning will be quite stressful for her to organise. But obviously don't want some immigration person to decide she can't come into the country (can't imagine why they would say no, as she is only coming to visit me, DH & the grandchildren, but you know the paranoia involved here!).

She has no criminal history, no history with immigration at all, so that's not an issue.

Does she need to get a visitor's visa ahead of time? Or just present her passport at immigration with the information on where she is staying (with us) until her return flight.

Just her passport and on the plane they will hand out landing cards to people without an EU passport, so she will need to fill that out. If she requires assistance they'll meet her at the plane with a wheelchair and someone will stay with her through immigration, pick up her bags and bring them through.
I'm sure all will be fine and I hope you both enjoy her visit,

Okay, thanks very much! One less thing to stress over! 

All she needs is her passport and her return flight. Arrivals hall can be horrific so it might be an idea to get assistance as Tykeman suggests.  My mother was always so obviously excited about seeing her grandchildren that she never had a bit of trouble at immigration. I'm sure your mother will have a great time.

Just clarifying, she will still have a visitor visa, it will just be granted at the border with a stamp on her passport. Most don't apply in advance for one unless there are concerns, like a prior refusal.

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I doubt they'll see your mother as an "overstayer" risk. She'll have a return ticket, make sure she has your address to include on the entry form and of course when she's asked about the reason for her stay I'm sure she'll be happy to tell the IO all about you and seeing her grandchildren!

We just did this with MIL.  It was her first time on a plane and came here all alone.  We booked her in for the service just so she wasn't alone.  Had a flight attendant encourage it also as sometimes the walking can be a it much.  SHe used the service on departure but felt good enough to take care of herself getting through immigration.  She's currently here for 3 weeks and I think they only asked her 1 question.