How to save all console output to file in R?

You have to sink "output" and "message" separately (the sink function only looks at the first element of type)

Now if you want the input to be logged too, then put it in a script:

script.R

1:5 + 1:3   # prints and gives a warning
stop("foo") # an error

And at the prompt:

con <- file("test.log")
sink(con, append=TRUE)
sink(con, append=TRUE, type="message")

# This will echo all input and not truncate 150+ character lines...
source("script.R", echo=TRUE, max.deparse.length=10000)

# Restore output to console
sink() 
sink(type="message")

# And look at the log...
cat(readLines("test.log"), sep="\n")

If you are able to use the bash shell, you can consider simply running the R code from within a bash script and piping the stdout and stderr streams to a file. Here is an example using a heredoc:

File: test.sh

#!/bin/bash
# this is a bash script
echo "Hello World, this is bash"

test1=$(echo "This is a test")

echo "Here is some R code:"

Rscript --slave --no-save --no-restore - "$test1" <<EOF
  ## R code
  cat("\nHello World, this is R\n")
  args <- commandArgs(TRUE)
  bash_message<-args[1]
  cat("\nThis is a message from bash:\n")
  cat("\n",paste0(bash_message),"\n")
EOF

# end of script 

Then when you run the script with both stderr and stdout piped to a log file:

$ chmod +x test.sh
$ ./test.sh
$ ./test.sh &>test.log
$ cat test.log
Hello World, this is bash
Here is some R code:

Hello World, this is R

This is a message from bash:

 This is a test

Other things to look at for this would be to try simply pipping the stdout and stderr right from the R heredoc into a log file; I haven't tried this yet but it will probably work too.

If you have access to a command line, you might prefer running your script from the command line with R CMD BATCH.

== begin contents of script.R ==

a <- "a"
a
How come I do not see this in log

== end contents of script.R ==

At the command prompt ("$" in many un*x variants, "C:>" in windows), run

$ R CMD BATCH script.R &

The trailing "&" is optional and runs the command in the background. The default name of the log file has "out" appended to the extension, i.e., script.Rout

== begin contents of script.Rout ==

R version 3.1.0 (2014-04-10) -- "Spring Dance"
Copyright (C) 2014 The R Foundation for Statistical Computing
Platform: i686-pc-linux-gnu (32-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

  Natural language support but running in an English locale

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

[Previously saved workspace restored]

> a <- "a"
> a
[1] "a"
> How come I do not see this in log
Error: unexpected symbol in "How come"
Execution halted

== end contents of script.Rout ==

You can't. At most you can save output with sink and input with savehistory separately. Or use external tool like script, screen or tmux.