diff --git a/Doc/api/api.tex b/Doc/api/api.tex
index b15c2d3..3d89adf 100644
--- a/Doc/api/api.tex
+++ b/Doc/api/api.tex
@@ -888,7 +888,7 @@
                                            const char *format, \moreargs}
 This function sets the error indicator.  \var{exception} should be a
 Python exception (string or class, not an instance).
-\var{fmt} should be a string, containing format codes, similar to 
+\var{format} should be a string, containing format codes, similar to 
 \cfunction{printf}. The \code{width.precision} before a format code
 is parsed, but the width part is ignored.
 
@@ -947,7 +947,7 @@
 
 \begin{cfuncdesc}{int}{PyErr_Warn}{PyObject *category, char *message}
 Issue a warning message.  The \var{category} argument is a warning
-category (see below) or NULL; the \var{message} argument is a message
+category (see below) or \NULL; the \var{message} argument is a message
 string.
 
 This function normally prints a warning message to \var{sys.stderr};
@@ -960,8 +960,9 @@
 an exception is raised.  (It is not possible to determine whether a
 warning message is actually printed, nor what the reason is for the
 exception; this is intentional.)  If an exception is raised, the
-caller should do its normal exception handling (e.g. DECREF owned
-references and return an error value).
+caller should do its normal exception handling
+(e.g. \cfunction{Py_DECREF()} owned references and return an error
+value).
 
 Warning categories must be subclasses of \cdata{Warning}; the default
 warning category is \cdata{RuntimeWarning}.  The standard Python
@@ -1104,7 +1105,7 @@
 \var{filename} is deemed interactive.  This is the case for files for
 which \samp{isatty(fileno(\var{fp}))} is true.  If the global flag
 \cdata{Py_InteractiveFlag} is true, this function also returns true if
-the \var{name} pointer is \NULL{} or if the name is equal to one of
+the \var{filename} pointer is \NULL{} or if the name is equal to one of
 the strings \code{'<stdin>'} or \code{'???'}.
 \end{cfuncdesc}
 
@@ -1497,22 +1498,24 @@
 arguments given by the tuple \var{args}.  If no arguments are
 needed, then \var{args} may be \NULL{}.  Returns the result of the
 call on success, or \NULL{} on failure.  This is the equivalent
-of the Python expression \samp{apply(\var{o}, \var{args})}.
+of the Python expression \samp{apply(\var{callable_object}, \var{args})}.
 \bifuncindex{apply}
 \end{cfuncdesc}
 
-\begin{cfuncdesc}{PyObject*}{PyObject_CallFunction}{PyObject *callable_object, char *format, ...}
+\begin{cfuncdesc}{PyObject*}{PyObject_CallFunction}{PyObject *callable_object,
+                                                    char *format, ...}
 Call a callable Python object \var{callable_object}, with a
 variable number of C arguments. The C arguments are described
 using a \cfunction{Py_BuildValue()} style format string. The format may
 be \NULL{}, indicating that no arguments are provided.  Returns the
 result of the call on success, or \NULL{} on failure.  This is
-the equivalent of the Python expression \samp{apply(\var{o},
+the equivalent of the Python expression \samp{apply(\var{callable_object},
 \var{args})}.\bifuncindex{apply}
 \end{cfuncdesc}
 
 
-\begin{cfuncdesc}{PyObject*}{PyObject_CallMethod}{PyObject *o, char *m, char *format, ...}
+\begin{cfuncdesc}{PyObject*}{PyObject_CallMethod}{PyObject *o,
+                                           char *method, char *format, ...}
 Call the method named \var{m} of object \var{o} with a variable number
 of C arguments.  The C arguments are described by a
 \cfunction{Py_BuildValue()} format string.  The format may be \NULL{},
@@ -1687,7 +1690,7 @@
 \begin{cfuncdesc}{PyObject*}{PyNumber_And}{PyObject *o1, PyObject *o2}
 Returns the ``bitwise and'' of \var{o2} and \var{o2} on success and
 \NULL{} on failure. This is the equivalent of the Python expression
-\samp{\var{o1} \& \var{o2}}.
+\samp{\var{o1} \&\ \var{o2}}.
 \end{cfuncdesc}
 
 
@@ -1745,7 +1748,7 @@
 \NULL{} on failure.  The operation is done \emph{in-place} when \var{o1}
 supports it.  This is the equivalent of the Python expression \samp{\var{o1}
 **= \var{o2}} when o3 is \cdata{Py_None}, or an in-place variant of
-\samp{pow(\var{o1}, \var{o2}, var{o3})} otherwise. If \var{o3} is to be
+\samp{pow(\var{o1}, \var{o2}, \var{o3})} otherwise. If \var{o3} is to be
 ignored, pass \cdata{Py_None} in its place (passing \NULL{} for \var{o3}
 would cause an illegal memory access).
 \end{cfuncdesc}
@@ -1767,10 +1770,10 @@
 
 
 \begin{cfuncdesc}{PyObject*}{PyNumber_InPlaceAnd}{PyObject *o1, PyObject *o2}
-Returns the ``bitwise and'' of \var{o2} and \var{o2} on success
-and \NULL{} on failure. The operation is done \emph{in-place} when \var{o1}
-supports it.  This is the equivalent of the Python expression \samp{\var{o1}
-\&= \var{o2}}.
+Returns the ``bitwise and'' of \var{o1} and \var{o2} on success
+and \NULL{} on failure. The operation is done \emph{in-place} when
+\var{o1} supports it.  This is the equivalent of the Python expression
+\samp{\var{o1} \&= \var{o2}}.
 \end{cfuncdesc}
 
 
@@ -1883,7 +1886,7 @@
 \end{cfuncdesc}
 
 \begin{cfuncdesc}{int}{PySequence_DelItem}{PyObject *o, int i}
-Delete the \var{i}th element of object \var{v}.  Returns
+Delete the \var{i}th element of object \var{o}.  Returns
 \code{-1} on failure.  This is the equivalent of the Python
 statement \samp{del \var{o}[\var{i}]}.
 \end{cfuncdesc}
@@ -2043,7 +2046,7 @@
 types.  Passing them an object of the wrong type is not a good idea;
 if you receive an object from a Python program and you are not sure
 that it has the right type, you must perform a type check first;
-for example. to check that an object is a dictionary, use
+for example, to check that an object is a dictionary, use
 \cfunction{PyDict_Check()}.  The chapter is structured like the
 ``family tree'' of Python object types.