I think you underestimate "pre-industrial" societies, and overestimate our own.  The technology may be different, but the people - and the problems - are the same.

Then why do we have more scientific and technological advances in the last century than in the previous 24?  We have something humanity has never had before, and that is the scientific method and the culture in which it exists.

Agriculture: To increase world food production by 34 percent (between 1951 and 1966), it took a 63% increase in money spent on tractors, a 146% increase in money spent on nitrate fertilizers, and a 300% increase in money spend on pesticides. To get another 34% would take even more money.

Do we need another 34%?  I understand that Monsanto has nitrogen-fixing maize (there goes your whole budget for nitrates), BT corn is only the first step (what were you saying about pesticides?), and tractors are only required by non-subsistence farmers.  Tractors last decades if properly maintained, and small tractors have been converted to electric propulsion with good results.

If you go to non-traditional crops, things look even better.  My (somewhat pessimistic) calculations indicate that you can grow 3000 calories/day of tilapia for 115 people on a hectare of algae pond.

Medicine: Despite the fact that we are spending more money on health care and medical research than ever, the American lifespan is not increasing much. The easy fixes - vitamins, vaccines, sanitation, etc. - have already been done. Now, we are struggling just to keep lifespan from decreasing (due to new challenges like AIDS).

I suppose it never occurred to you that AIDS, heart disease and lung cancer are mostly behavioral diseases.  Serve green salads instead of french fries and spend enough time harassing smokers to quit and promiscuous people and IV drug abusers to change their ways, and those problems shrink with no medical advances at all.  Of course, you might not like the liberty costs.

Outside those areas, science still yields dividends.  There have been recent developments in vaccine production, to give one example.  Using fragments of DNA instead of whole viruses and multiplying them in vats rather than growing them in eggs could produce a year's worth of vaccine in days or weeks instead of months.  The major obstacle there isn't scientific or technological, it's financial/bureaucratic.

Science: Most of the great work of science was done years, even centuries ago. Many of the greatest contributions to science were made by people without formal training. But the day is past when monks growing peas or people flying kites in the rain can make significant contributions to science.

Oddly, we are still getting original contributions to science and mathematics from entries in high-school science fairs.  Only the creme de la creme, of course, but they exist.

The specialist knowledge remaining to be discovered requires expensive education, for relatively little return. Something like 90% of all the scientists who have ever lived on earth are alive right now, yet technological innovation is slowing.

You conflate science with technology.  Technology uses science, but scientists do not typically create technologies.

The pace of technological change continues to accelerate in many areas; just look at the announcements over the last 2 years in photovoltaics, batteries, and biotech.  (That's just what I've been looking at; there's much more.)

Oil: In 1950, one barrel of oil's worth of energy could get you 100 barrels in return. Now, it's more like 1:10 in the U.S., 1:30 for Middle East oil shipped here. That sort of decline applies to most resources: coal, copper, natural gas, etc.

What does a kWh of energy into a wind turbine get you back?  What are the prospects for coppiced willow shrubs, or Miscanthus Giganticus?  (They're perennials; you plant them, and they produce for 10 years or more.)

R&D: Technology has saves us in the past; can it save us again? Probably not. Analysis shows that an increase in spending on R&D of 4.2% yields an improvement of only 2%. At that rate, even if every one of us becomes a scientist or engineer, we'll be losing ground.

Sounds more to me that there's a limit to the pace at which human institutions can absorb change.  Since it is obviously drawn from historical data, it cannot mean that there is some end point beyond which we can't advance; we've never seen any such thing, and such a conclusion cannot be supported by experience.

More likely, it means that we've got X fraction of people who are effective at R&D; once they are fully employed, spending more money means bringing in less-effective people who yield less for the expenditure.  No mysteries there.  Creating better analytical and other development tools will increase productivity across the board; the easier they are to use, the more people will see greater productivity.

Government: Increasing complexity means increasing bureaucracy, and all the expenses that entails.... Generally, the tipping point is about 20% - which we're past.

I completely fail to see how advances like better vaccines, improved PV systems or Buckytube wires for electric transmission require more complex government.  Lots of things would be improved by a less complex government, with fewer loopholes and preferences for existing special interests (which are threatened by innovation and tend to oppose what they don't control).

You see what I mean?  It's not that we won't continue innovating.  It's that it's taking more and more work, more and more energy, more and more resources, for less and less benefit.  In the face of peak oil, we will not be able to continue down that path.

I understand you, it's just that I'm absolutely certain you're wrong.

We would not have commercial air flights now if it weren't for government support.  We would not have any transportation systems at all without the government.

Hah.  Private turnpikes in the USA date from 1795, and of the major modes of transport over the last 20 centuries, government invented exactly zero of them.  The first airfields were private, the first railroads were private, the first steamships were private... I have not studied the matter, but I would not be surprised to learn that the first barge canals were private.

Government serves best by studying to see if the public interest is best served by a particular type or direction of development, setting up non-discriminatory incentives if it is, and then getting out of the way.  Fix global warming?  Set up a comprehensive system of GHG emission taxes and sequestration credits, get out of the way.  If government has done it right it will cost to do the wrong thing and pay to do the right thing, and people will stampede to do the things that pay.  The people who set the policy don't have to know how the ends will be accomplished, only that the benefits are restricted to those actions which accomplish them.  What gets rewarded, gets done.